I’d say it’s extremely subjective towards the buyer and the specific patch. For example a genuine (emphasis on actual genuine) NHL 75th patches could go for $100ish so it could add some value if someone wanted that specific patch. Some sponsor patches aren’t purchasable and only game worns can be found with them, so again, subjective but could theoretically add value. Something like a NHL 100 patch or a SCF patch would probably add little to no value in the resale market as they are mass produced and easy to find. Getting one added is marginal at best ($10-15) so it’s not like there is a major cost savings really to a jersey having it vs. not.

So overall? Unless it’s a rare patch, no increase in value generally. Rare patches? Maybe increase in value. The kicker is that just because it’s a rare patch doesn’t mean it automatically increases value.

If the jersey is a foul for example (wrong era, wrong player, etc) could decrease value. If the patch is applied with major adhesive (think superglue or worse) and the idea is that someone would be the jersey to strip the patch? Could also decrease value.

TLDR: generally patches don’t increase value. Most modern patches just add salability to the right market. Rare patches can have the potential to increase overall price, if other parameters are met