I suggest you start by observing carefully.

I see it this way:
you got a few potential issues
1. interaction with other species. In a 20 gallon that's likely to lead to problems with anything that's not a strict bottom dweller.
2. Swimming space. Not much you can do there except upgrade.
3. interaction between the tiger barbs. Here's where uncertainty sets in. I've seen this species build up a hierarchical structure that reminds me of birds. There's one or two boss fish, quite a few in the middle and one or two that are at the bottom of the school. If those bottom fish do not get harassed so much that they suffer physical damage and if they still get a chance to eat you do have a shot at pulling this off.
On the other hand, I've also seen them where 2 or even 3 distinct groups formed and there was constant bickering. That stresses everyone out

Even if you do manage to get a school that works well you sitll have the issue of a relatively low amount of swimming space that I feel you need to address sooner or later.

But, this is just my $0.02.