There are conflicting accounts on why he did this. The most fundamental thing that all sources (at least the ones I've access to) agree on is that Stalin never actually expected to be removed. As general secretary he acted as a middleman between local party organizations and the centralized party, so for years before Lenin's death he'd been effectively the only channel by which the leaders of local party organizations had interacted with Moscow. This gave him exceeding importance which was massively underestimated by his political opponents. The first account we have of him attempting to resign is in light of Lenin's recommendation that he be removed from the post of general secretary as he was "rude" and should be replaced by someone "more agreeable and considerate of the other comrades". At this point, Stalin was not in any way considered head of the USSR as he would be by the mid-30s, so the party refusing to grant his offer most likely came from a lack of eligible replacements (after all, Stalin had spent years near single-handedly organizing the party to collaborate with him from the bottom up) and Stalin's political opponents vastly underestimating his ability to control the party from his posting, and making that posting so essential to the state apparatus of the soviet union.

All later accounts of him offering (or rather threatening) his resignation, to my knowledge, are after he'd effectively 'taken power', and consolidated it through the purges. At this point, the party existed more or less in a state of complete adherence and loyalty to Stalin. The threats of resignation at this point resembled more a game of loyalty than anything else. By the most reasonable analysis Stalin saw these threats as tests of loyalty to those in the position to grant his wish of removal: if they approved, they could immediately be accused (in the patented stalinist style of twisting reality) of attempting to remove the great leader and trying to take power themselves, and whatever labels or counterrevolutionary activity would come with such a charge. Therefore, every offer (or threat) of resignation that Stalin ever dealt after he'd consolidated power was met with rejection, by some accounts even begging him not to abandon his posting as general secretary.

There was, of course, another layer of utility to these resignation offers. Whenever the party would reject him, it acted not only to show their loyalty to Stalin's person, but their agreement to his policies. The central committee repeatedly telling Stalin that he was ideal in his position as general secretary reflected that yes, his work so far has been good enough to keep him in this position. Therefore, not accepting the resignation offer eliminated their ability to contest Stalin's policy decisions; after all, they had been the ones who appointed him General secretary over and over again.

So basically to answer the substance of your question. Did Stalin offer to resign? Yes. Multiple times in fact. Why did he want this? He didn't. At least, he didn't want his offer to be accepted. Each time he did request his removal, he took a calculated risk in hopes of attaining the benefits of being turned down. Could the party truly have removed him? The first time he offered, yes, most likely, but at a severe cost to party cohesion. Later on, you really can't say, as Stalin was definitely in a position to remove those consenting to his would-be resignation. Either way, his goal always was to get reassurance either of his position's stability or the loyalty of his underlings, as well as implied consent to his decisions. We can say with reserved certainty that he never wished for his request to be granted.