Hi,

I do recommend bringing extra tubes because sometimes you can get a flat where you (1) can't find the puncture (easily enough) or (2) you found it and you can't fix it.

If you can find and fix the flat (and you aren't in a big hurry), then patching is perfectly fine thing to do. If you are on an organized ride, it's probably better to swap in a new tube if they are waiting for you and then patch it at home.

Cheers,
Charles