Hi John,
If there is the possibility of a cross-feed - allowing you to connect the two tanks together, then yes. Otherwise no, and the risks should be small, but:
Even if the switching valve was designed to be mechanically incapable to cross-feed, then you still need to consider the effects of wear or manufacturing problems - then you could experience a pressure leak from one system into the other.
But from the sound of it, you don't have any gauges in the pigtails - so really the only item we need to consider are the two rubber pressure seals on the Butane supply - the one that links the pigtail to the Camping Gaz adaptor, and the seal between the Camping Gaz bottle and the adaptor. Simply make sure those seals are in good condition and replaced when necessary...
If you had a good quality system installed, with a switching valve that prevents cross-feed, and the system is checked and maintained - then any risks must be very small indeed
For risk comparison, the brass seal surface of the bull-nosed POL connector is very easy to scratch (say from a small piece of grit picked up in the locker) and then that scratch means a leak between the Propane bottle and the pigtail - Now I've seen that issue more than once at an EribaFest, where someone runs out of Propane over a summer weekend - and I'd rate the risks of a Propane leak around the brass POL connector to be much higher than a cross-feed problem...
And it's a good idea if the pigtails have non-return valves at the end you connect to the gas bottles...
Robert