I am not positive, but I think the aquiring signal message may be associated with the inReach communicating with the Iridium satellites - the GPS signal comes from a different satellite system.
In mountainous terrain I have noticed that if I am in a deep valley I can get an "aquiring signal" message and that messages sent don't get sent out while the unit is "aquiring signal".
I have also noticed that the "aquring signal" messagee seems to coincide with the unit not flashing the signal LED which according to the manual (yes I did acually read it), indicates lack of communication to the Iridium satellite network.
Iridium is a LEO (low earth orbit) satellite matrix, so even in deep valleys with limited view of the sky there "should" be times when a satellite is overhead - although coverage could be quite limited in really deep valleys.
In case you haven't noticed Delorme is releasing a new version of the inReach this month with an integral display - undoubtedly this will be more convenient for self propelled activities, but will be missing some of the funtionality provided by the smart phone interface. The good news is that it will still support the smart phone interface so when the additional weight and bulk of your smart phone are not a issue you will still be able to use it.
I am very happy with my InReach, with the exception that for many of my adventures I can't justify the weight of packing a smart phone, so have to rely on the pre-programmed messages only. I am planning on picking up the new inReach SE with the integral screen once it has been on the market for 6-12 months.
As for performance of the GPS function it does not seem as sensitive as my Garmin 62S, but I have seen Earthmate state accuracy to +/- 5 m.