Per the Minecraft Wiki's entry on Far Lands:
As the player journeys even deeper into the Far Lands, the effects
worsen to the point where the game is unplayable. At X/Z
±32,000,000, block physics stop functioning correctly. Lighting
doesn't work and the blocks, although they appear to be there, aren't
solid. If the player tries to walk on these blocks, he or she will
fall into the Void. At excessive X/Z positions, world renderer no
longer works, or takes incredibly long times and uses most, if not all
CPU usage. It then becomes almost impossible to close Minecraft
without a task manager.
So, yes - eventually, if you go far enough into the Far Lands, Minecraft becomes less and less responsive to the point of the only solution being to kill the process.
As for whether a 64-bit processor vs 32-bit changes anything? Doubtful, although the trivia section does include this bit of info:
The highest signed value for 64-bit machines is X/Z
±9,223,372,036,854,775,807. However, despite this being the limit any
machine can go, it may not be possible to reach anywhere near this
point, since the vast majority of people experience instant client
freeze, followed by the client crashing. If teleported there, the
screen will display completely black with no sun and oddly glowing
So while it sounds like it is conceivable to go that far, Minecraft would probably cease responding long before.