I don't think so.
Recently on itinerary LHR-FRA-SFO-SNA i was able to OLCI on FRA-SFO leg.
LH wouldn't let me to OLCI, because I was flying on UA ticket so I had to use LH check-in service at LHR. My luggage was tagged all the way through to SNA, but LH gave me only BP to FRA.
At FRA UA agent gave me BPs for FRA-SFO (in addition to one printed using OLCI) and also for SFO-SNA segments.