Not necessarily. Yes, it's true that in this era the Emperorship essentially had to be bought, even by the Hapsburgs when they had their monopoly. But there is a chance. I remember that for the 1519 election, the Pope really didn't want a Hapsburg to win again, so he sent entreaties to Elector Frederick of Saxony, telling him that he would pardon Martin Luther of all sins and personally would help fix the election if Frederick would stand against Charles. Frederick, of course, refused. However, this election is very close to when Henry wrote Assertio Septum Sacramentorum (1521) and was named Defender of the Faith. The Pope had no more love of the French - they had been interfering in Italy just as much as the Spanish had, recently - but if you can find a way to swap events round so the election is delayed, or Henry writes his book two years earlier (which means Luther's events happening earlier too) then it's entirely possible that the Pope, frustrated at Frederick and Luther, would then turn against them and ask Henry to step in. If Henry has the Pope's help, he could turn a few electors. I seem to recall that Henry actually did put in his own money for winning the election, too (iirc he spent £90,000 of taxation money on failing to bribe several electors) so he was clearly willing to do what was needed.
Of course, how good a HRE he would actually be is entirely another point. If you want him to actually do fairly well, you may need to somehow give Henry some land on the continent (as close to/inside Germany, the better) to act as a power base, even if it's not one of the big Electorate states. Henry keeps Tournai rather than selling it back to the French, maybe?
Because he knew he wouldn't win, pure and simple. His involvement was token. I know he did give some bribes, but they were probably either to win a single Elector for the prestige, or simply so that his candidateship didn't look like he was just showing off by pretending to be involved (which was of course actually the case). But he knew he wouldn't win, so he wasn't concerned about it.