Root with Stock Recovery?

Hi folk,
Ok, it may seem a silly question, but I did search in previous posts, and and didn't find out an answer.

Now easly: can I root with the custom recovery loaded on the fly (fastboot boot TWRP.img), that's not flashing it into the recovery partition?
Does it keep the root on, and together the chance to OTA?

Or do I need to flash the custom Recovery in any case?
In this case, how can I make a "my_recovery.img" dump from my original?
I tried loading on-the-fly the TWRP, and selecting backup, but I got a lot of files ....

Thanks, sorry if these questions were already asked, but I didn't find any answer...