I've been running a similar volume - around 10k invitations a month across my own accounts and client campaigns. Ended up with roughly 11 verified, engaged profiles from that batch. The real issue isn't volume though, it's targeting and the sequence after the connect.
Most people blast invites using a broad demographic filter and call it "scale". That's just noisy data. With that kind of volume, your acceptance rate will tank unless you layer in intent signals - job changes, shared group memberships, recent content engagement. We saw a 3× improvement when we shifted from role-based targeting to firmographic + trigger events.
What's your primary objective? Pipeline generation, brand awareness, or list building? That changes the entire strategy. For pipeline, I'd rather send 2k highly sequenced invites with custom note templates per segment than blast 10k with a generic "I'd like to add you to my network".