FTL blockers probably don't stop gateway travel (and it probably shouldn't either, since gateways are hardly traditional FTL), but OP is talking about hyperlane travel between L-gate systems, and from personal experience, arriving in a FTL-blocked system via non-hyperlane means that you can't use any hyperlane in it until the blocker is destroyed. Happened to me quite a few times in the past while jumping in a FTL-blocked system with jumpdrives. Maybe it changed since then, though.
Then again, the L-cluster seems to have a few odd quirks in that regard (I'm pretty sure sensors don't work either in there, I remember building a listening post in Terminal Egress while I was still fighting the Grey Tempest and I couldn't see any system past it), so who knows what's the actual intent here? It's probably worth posting this in Bug Report, just in case.