I don't have a TRAX yet but I expect to buy a 2017 when they hit dealers.
I'm very interested in the towing topic. I'm hoping some engineering minds are reading this thread and can give us some real details.
FIRST... do not take my advice as there can be very serious consequences to not following manufacturer's guidelines regarding capacities and use-cases for equipment such as cars.
While I don't know many technical details about the TRAX, I do have experiences towing with many vehicles.
So as far as the original topic at hand I do believe that the TRAX is certainly capable of towing some things, but there isn't enough information in the original post.
How much does it weigh?
How much tongue weight?
Does the trailer have brakes? What kind of brakes?
How tough are the towing conditions? (Up hills? Highway speeds? Summer heat?)
What else will be in the vehicle on one of these trips? (your 3 fishing buddies?)
I'm saying that the TRAX can certainly tow a 4x6 utility trailer with a couple of bags of mulch to/from Lowe's with just you in it, and the TRAX certainly CANNOT tow a 17 foot inboard ski boat with your wife, 2 kids and Labrador along with a cooler of beer inside the car and a kayak tied to the top.
My first concern is the connection points for the hitch. The eTrailer website shows several Class II options. I'm thinking that if the manufacturers are willing to rate up to the stated 2000 lbs, then the connections are probably OK up to that weight. The Chevrolet branded hitch is NOT suitable for towing and only an aftermarket hitch designed to be used this way should be installed if you plan to tow. I would not trust the connection points on a hitch that doesn't state a tow rating for a specific hitch/car model combination (that part is very important).
My next concern is braking power. Without trailer brakes, you want to be sure not to exceed weight equal (or nearly equal) to what the car is intended to carry (people, gear, etc.). So this is why you alone and a 4x6 trailer with mulch is fine because all of that together isn't really exceeding the intended carrying capacity. Braking power for the car can't really be significantly "upgraded" so adding brakes to the trailer would be the solution. There are various trailer brake types that are suitable for different purposes.
My next concern would be tires. I'm not sure what tires come on the TRAX, but they likely are on the lower end of all specs.
Then handling is a real concern. I feel like this is where people say something like, "the tail wagging the dog." You don't want a load that your TRAX can't control. This has a lot to do with speed and the shape of your trailer/cargo. Winds on the highway for a trailer can be very significant. A utility trailer vs. a camper trailer are very different beasts for this reason (a boat can also catch a lot of crosswind). Beyond wind is just simple trailer sway, which can be caused by things other than wind (such as oversteer). Being prepared (you) to handle trailer sway is very important, even when properly equipped. Some of your normal driving/physical instincts may cause you to react improperly--this is one of those knowledge/experience things.
Related to handling is load/weight distribution. Be sure you know how to load the cargo correctly for the best trailering experience. This includes getting the ball height correct for your trailer. If you wanted to get fancy, you maybe can even get light duty weight distributing components for your trailer and hitch (compatibility can be tricky). Weight distribution components can greatly improve handling. Also, the cargo distribution in your car could matter too, primarily on the rear suspension--don't put a huge beer cooler in the back along with a heavy trailer tongue.
All of the reasons above are very clearly safety concerns. Be sure you are VERY comfortable and have a thorough understanding of each of those issues and how they relate to your towing scenario before you decide to tow. The stuff below, though might loosely have safety implications, is really more about protecting your investment (your money).
Now that the more important stuff is addressed, I would start worrying about the drivetrain. For this, it's heat that is the major concern. Towing is going to increase what your car is doing, and therefore everything is going to get hot. If you plan on driving over many hills, or plan on really pushing the weight (maybe in excess of 1000 lbs), or plan on towing on really hot days, then you should probably address this. You can have a transmission oil cooler added. You might even be able to put on an engine oil cooler. The fans on the radiator for the engine coolant may also be replaceable to bigger models (or there might be room for additional fans). You could go as far as adding temp gauges so you can monitor these components.
Liability... make sure that you are reasonably sure that you aren't doing something that won't be covered by your insurance when something happens.
And lastly, there is the warranty. I recommend buying a hitch-mount bicycle rack and putting it on your car every time it goes to the dealer. "Towing? Oh no... that's just for my bike rack."
Again, do NOT take my advice because using the car outside its intended capacities or purposes could be very dangerous.
My personal opinion (only opinion!) is that cars today get such low ratings because of our litigation-prone society. Towing a trailer takes knowledge and can be done safely. It can also be done very dangerously by someone without the proper knowledge, regardless of the equipment they're using.
One more disclaimer... if this didn't sound like stuff you already knew, you should seek out a lot more knowledge before you tow a trailer.
SHEW! That's over. If I buy one of these things in a few months, I can promise you that it's getting a hitch (and a bike rack!).