Go with "everything seeming OK" as your first clue.
I'd agree with Rohit that providing some support for the plants would be good, in part because it will give them more room vertically before they fall all over themselves.
Yields will be less-per-plant than if each plant had more space. But overall yields probably won't be much impacted, unless you get visited by disease. When or if blight comes to you, it will have an easy time spreading through all the plants with them closely spaced and intertwined. But it's hardly certain that chopping out half the plants would really change that much in a small planter.
One approach I'm guessing you are not taking which you might consider for next time is stake or string support combined with aggressive pruning (removing suckers and training to a single, supported stem) for an indeterminate variety like Super Sonic. Where you have space and time overall fruit yields can be higher (but generally later and smaller fruits) with a "let it go wild" approach - the single supported stem gets you generally earlier and larger fruits, that are easier to harvest (or even find, when an overgrown indeterminate really gets tangled up) with better airflow between plants which reduces the fungal disease issues that tomatoes are prone to.
You could head off side branches (and their own small suckers) and choose to start pruning your main stems down to single stem for the remainder of the season if you establish some support for them, but I would not just hack off the existing side stems if they have fruits developing. I would take an aggressive approach to any yellowing or browning leaves on the lower part of the plant, however, and remove those ASAP, (assume fungus and try to remove before it makes more fungus and spreads further) as well as pruning off the side branches you have headed off (if you do that) after their fruits are done.
