Just removing the carbs is going to upset the synchronization to some extent; although it shouldn't be much.
I would suggest trying to determine which seal is leaking first. If it is only the bowl mount seals; they are reasonably practical to change on the car, and doing so won't disturb any adjustments. Fairly easy too, as long as you are good at working by touch. Mine seem to only last a few years at best, so I've gotten pretty good at changing them. (Maybe next time, I'll try some of Mark Macy's polyurethane ones.)
Jet seals are more difficult to do on the car, although still quite possible. But you have to disturb the jet centering to get them out, and most likely you'll need to tweak the mixture after changing them. The upper seal leaks fuel into the carb throat, so it screws up the mixture.
Personally, I prefer to set the mixture full lean while checking the jet centering anyway, as that provides a 'worst case' check and ensures they are centered well enough to avoid wearing the jet/needle during normal operation. Worn jets (due to improper centering) are a frustrating and apparently common malady, that can lead to overheating and worse. (Dad's TR3A once scattered engine internals all over the highway, due I believe to worn carb jets.)
If you've never been in there before, I would suggest also changing the spring that goes between the two jet seals. It's not unusual for original ones to be weak from age and corrosion; or to have been distorted by a previous owner frustrated with constant leaks. You'll have to buy the springs separately, they don't come with the kits.