As worded? I'd say no.
Worded differently, for the same (or very nearly the same) effect? I'd say yes.
"Immediately before my next turn" isn't a perceivable action/incident.
"Immediately after {the player before me} moves/attacks/casts/whatever", very likely is. Your order there might get a bit mixed up if, for example, you pick 'moves', and the target player moves and then attacks, but even that is effectively the same thing.
You're still running the risk that some action prior to the action that triggers your readied action is going to change things such that the action is useless/pointless/impossible. If you want to trigger off of 'Bob the Fighter' attacking an enemy, and the enemy caster throws down a Wall of Stone between the two of you, you've lost your ability to trigger off of Bob's action, unless he can move back into sight.
Remember, too, that readying an action isn't a subtle thing. The enemy may not know exactly what you have planned, but there's probably several cues as to what you're waiting for, and what you're planning to do in general terms. If you're waiting for Bob to attack someone, you're going to be watching Bob pretty carefully. If you're planning to stab someone, you're going to be paying attention to them as well. If you're planning to run somewhere, you'll probably be keeping an eye on the general path there to make sure it doesn't get blocked. (Or at least that you won't be completely surprised when it happens.) If you're going to be shooting someone with an arrow, you've got it nocked, and drawn back, ready to loose when the trigger occurs.
Observant enemies can see these sorts of things, and realize that something is going down. If they get lucky, they can guess what it is with some degree of clarity, and act to minimize the risk that action presents. This might be where passive Insight or Perception come into play, though I'd have to give some thought on how I'd set the DCs. If the DM does this, however, it's got to go both ways. PCs can notice those same cues, and have a chance to interpret them to their advantage misinterpret them to their disadvantage.