Yes, one three-jump competition is allowed in a free skate. It can include any three jumps that would be allowed in the program. (I.e., you can't do 3T+3T+3T because it's only allowed to perform the same jump at most twice.)
Here's an example.
However, with no bonus to the base value for difficult combinations, is it worth including a combination that is likely to earn lower GOE and that uses up three triples all in one jump pass?
If you only have five triples in your repertoire, with two repeats for a total of seven, you could use up all your triples in five jump passes (or four if you include another 3-3 combo) and only be able to use double axels and easier doubles in the remaining jump passes. It might be wiser to spread them out in hopes of better GOE.
For a skater who does triple axels and/or quads, then a 3-3-3 would make more sense in terms of maximizing base value, possibly beyond whatever loss of GOE it might entail.
Same issue with quad-quad combo. Will it lead to using up the quads in your repertoire in fewer jump passes and leave other jump passes only that can only be filled with low-value jumps? In which case, it would make more sense to spread out the quads and most likely earn higher GOE.
For a guy with multiple quads who is already leaving out easy triples, it might be worthwhile.
But what would really make these things worthwhile would be either some bonus for the difficulty of the combination beyond just adding the base values of its constituent jumps, or else the possibility for skaters who use up all their triples (and double axels, for women) in less than 7 jump passes to replace the remaining slots with non-jump elements that are worth more than double jumps.
For the quad-quad, maybe someday it will be allowed in short programs, where it would definitely be worthwhile. But I don't expect that to happen until several guys have shown it in freeskates, which they won't do unless there's a big reward for doing it there to offset the big risk.
Re quad-quad, only Nathan Chen would seem to benefit from doing a quad-quad. Comparison of jump layouts:
Current layout:
4Lz
4F
4T
3A
4T+3T
3Lz+3T
3F+Eu+3S
New jump layout:
4Lz
4F
4T+4T
4S
3A
3Lz+3T
3F+3T+3Lo
This would be a bit of a silly layout, but it would replace Eu + 3S with 3T + 3Lo and a 4S for a 3T. The net effect is replacing a Eu+3S with a 4S, 3Lo which is more than a free 4S. Given that Nathan has trained 4-4 and 4-3-3, my plan might be on a similar track to what he's training.