On a PCB, can an antenna for 433MHz RF be "far" from the transceiver?
As with all engineering problems -- that depends.
If you had a nice well-mannered antenna that presents a 50-ohm impedance (or any known, controlled impedance) at its terminals, then you could make a controlled impedance trace with that impedance back to the tranceiver.  Then the only thing you'd have to worry about is the leakage from the trace, and the loss in the board.  If you had a multi-layer board you could sandwich your trace between ground layers for much less leakage.
I would be careful about putting components close to the transmission line.  If you're just using a single trace operating against a ground plane, then it'll have fringing effects that really never go to zero, but which probably drop off rapidly once you get further away than twice the width of the trace or twice the thickness between trace and ground plane, whichever is further.  But the effects will never really go away -- so you wouldn't want to place sensitive components close to it (I'd build a board just for the experiment, and fire 433MHz through it and test how much various things placed at various distances picked up).
Without a lot of experimentation, I think that if I did do this I'd clear an avenue for the trace (perhaps along the edge of the board) and run it there.  Or I'd just figure out how to place the tranceiver right next to the antenna, and bring the (presumably much slower) signals to and from it to wherever they need to be.