It depends on the tech. For some things, mainly abilities and ship research access, you need to keep the labs around. If you lose them, you'll no longer be able to say build heavy cruisers or fire super weapons. For other things, mainly say armor and weapon upgrades (most things that give +% bonuses), stay around even after you loose the labs.

Thus you can scuttle a few labs after your research everything. That is a handful of civic labs (unless you're advent, then its the opposite), as your superweapon will require 8 military labs. Note you won't be able to build things like trade ports if you scrap them all though.