You can certainly crosscut 2x stock with a track saw. The depth of cut on the TS55 (and most competitors) is just over 2".
You'll probably want a few things to make the job easier, though.
You'll definitely want some way to support both your workpiece and the offcut. This can be as simple as a sacrificial sheet of MDF or rigid insulation.
The MFT-3 comes with a fence and rigging to hold a track. This will let you accurately cut 90-degree angles and support your workpiece. You'll still need something to support longer offcuts, though.
There are also squares that you can attach to the track to allow you to set up more quickly than the MFT-3. (Here is an example.) You can couple this with a very small section of track (cut down from what Festool sells) to use specifically for crosscutting.
If you're mainly going to be working with 2x stock doing rough framing work I'd suggest looking at the HK55 as well. It's a non-plunging track saw that's attached to the track. It's specifically designed for crosscutting.