Apologies for the contradiction in the title, it's the best way I could think of to word it!
I need to randomly allocate participants of a survey to see either question X or question Y. However, I need to use block randomisation (i.e, for a block of 4 participants, 2 will be in X and 2 in Y). Is this possible within Limesurvey? I know that I can easily implement randomisation whereby each participant will be randomly allocated to X or Y, but I run the risk of an imbalance, or long streaks of imbalance at least. I'm inclined to think it may not be possible, as I think it requires that the survey somehow keeps track of the previous allocations and I'm not sure how to achieve that.

Any input would be appreciated, I'm really just scoping this out right now.

You are correct - this is not possible with core LimeSurvey. There is no way to know how many COMPLETED responses have been assigned to a particular "stream".

I suppose you could make an AJAX call to a remote PHP script that queries the database but that would require some development and would not be able to account for concurrent incomplete responses,