I use the "add inflight aircraft", and the helo is in-flight as designed. I've used the mission designer quite a lot, and can't find any logigal reason for the helicopter not responding. Like I said, it works from time to time, even without changing any parameters. I have the newest DW patch, and the problem remains the same despite the LWAMI mod patch number. I figured it might have something to do with the helo's tactics (transit/transit search etc).
Can't remember if I have used this in any Future Fleet missions currently in Bill's site, but it seems that the majority of designers don't have this problem. (Should I perhaps make the helo a controllable platform? This may cause some problems in the solo missions that I make.)
I guess I'll just use the helo as intended, and if somebody other has the same problem during gameplay, remove the in-flight helo option. I'm currently in play-testing phase of 7 new FF missions, and in a couple of them it would be nice to have the helo already in the air.
Thanks for the answer, anyway.