In Blitz games, with very little time left for both players, is it acceptable to keep on checking the opponent and waste their time and win the game on time? Is that true sportsmanship?
Time is a resource in blitz chess, as much as or even more so than material. If it isn't unsportsmanlike to capture your opponent's material, how is it unsportsmanlike to capture their time?
In blitz chess, there is often a time-endgame. Otherwise pointless checks and random-looking moves are part of this endgame. From my perspective, this is part of what makes blitz fun. I have lost many blitz games because my opponent found ways to make me burn precious seconds responding to annoying checks at the end of the game, and have never thought of them as bad players for doing so.
waste their time
If it's clear that they are able to win within the time they have left, this could be considered bad sportsmanship. However, in those situations the number of remaining checks is usually quite low.
win the game on time
If that's a possibility, I'd say it's perfectly fine to play on if you're losing on the board. At the beginning of the game, both players get the same amount of time to finish the game, not just to obtain a winning position. Time management is an important part of the game, and if you fail at it, you deserve as much to lose as you do with failing to obtain a good (or drawn) position.