Tobias, to answer the question I believe you are asking, "Would it be cool if you jumped into my group if we had a spot open?" Unless I have 3 other players in my group (assuming that the max is 4 total per group), the answer is and always should be, "Absolutely!", even when done in the virtual sense of claiming that open tee time on your app.
I'm at a club now that gives members the chance to freeze people out of a tee time once one person has reserved that time for themselves or however many playing partners they want to bring along. This makes finding spots to play difficult on busy days, and nearly impossible on weekends and holidays. I'd be thrilled to join up with a twosome or threesome if it meant getting to play.
On the flipside, I don't have a group that I play with, so oftentimes I'm forced to play as a single, stuck in-between larger groups during the round. However, I usually use that to my advantage as I use it as an excuse to join up with a group in front or behind me as a way to speed up play for everyone. I've been lucky so far as I've been able to join up with some of the same folks a few times now, so we're familiar with each other and have a good time playing together. The times that I have brought along a playing partner or two, I'm quick to ask that single teeing off in front or behind us if that want to join up.
To me, playing the game with others is how the game is intended to be played. I'm not lucky enough to have that group of golf buddies that play together on the regular, but even if I did I would never allow it to be the case that we only exclusively play together, excluding anyone else that might want to play with us.
You're not being rude or annoying by taking that open tee time. Sharing the game of golf with others is the best way to play. Those that would exclude or shut you out show themselves to be the ones who might be categorized as "rude."
