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That depends on how you define reasonable. I guess it would only reduce its strength by about 150 Elo compared to non-extreme time controls of the same average time per move. (Of course the opponents would likely also suffer, and it is difficult to predict if they would suffer more or less.) That is at least more reasonable than reducing its strength by 2500 Elo through making it search 1 ply only.

The reason is that engines function optimally if they can allocate time to those moves where it is needed. This results in a strongly variable time per move: there are natural points where they could stop, and time spent after that is largely wasted, until you go all the way to the next point where to stop. Unless they discover that they are really in trouble, i.e. the move they focused on so far suddenly turns sour at larger depth. Then it pays to allow them extra time until they found at least a reasonale alternative. After all, time is only a factor if you plan to fight on. So playing a move that you know to be immediately losing just to save time is never an attractive proposition.

By harrassing the engine through facing it with a time control on every move, you largely make sensible time management impossible. In particular, Joker calculates its nominal search time as T/(N+3), where T is the remaining time on its clock, N is the number of moves it still has to do in that time. So it keeps 3 moves worth of time reserve to be able to solve inadvertant trouble on the last move before the TC. But if N=1 always, this would make it do the initial moves very fast.

I would advice against trying extreme time controls, but use the engines in modes for which they are designed, rather than see how much you can stress them before they break. At least, I assume you are interested in how well they play Chess. If you put two grand masters to a game where someone is constantly knocking them over the head with a pillow, and hosing them down with a fire hose... Well, they might be able to complete the game, but who wins is likely to reflect other properties than their skill at chess. Just play game/time, game + small increment per time or 40 moves/time. So 15+0, 10+5 or 40/10 would be good controls to test them at (i.e. 15 min sudden death, 10 min + 5 sec/move or 40 moves / 10 min). Trying extremes only tells you something about the robustness of their time management outside the range of its design parameters, and has little to do with chess.