When do pilots use NOTAMs?
Use or check? NOTAMs can give pilots of a wide range of information, so in terms of use each NOTAM is different. For example, they might tell the pilot that a frequency has changed - so that's something they may need to integrate into their flight at the relevant point.

Or, the classic, is that there are standing NOTAMs in the UK that overflying Ukraine and Syria aren't recommended. Not something most pilots need to worry about.

There is no expectation to check NOTAMs after departure, however.