Here's what I've experienced...
Even if you have a FOH/sound engineer who is very amenable to what you want to do, that person's job first and foremost will be the live sound for the band. What that means is that he/she will get busy and there will be the inevitable situation where he/she has to choose between making sure the tape rolls or making sure the live sound is right.
Venues that have a DAT deck already hooked to the system (and actually working), you're likely to have no problems. Other times, the sound engineer has to rummage around to find a connection, set up the recording device and work to make sure the levels are correct. Unless it's important to the band that tape roll for the show, it will be one of the sound engineer's lowest priorities.
Now, after I've written all that, let me say that I have met some terrific FOH guys who will bend over backwards to record the band they're working with...even if it means hanging a couple of SM57's off the front of the board to get a recording.
One option you might consider is if you were able to get the itinerary of the band and then try to arrange to have people in other areas cover the shows for you. You work out the logistics for the recordist (access to the show, who to contact, phone numbers as needed, blank media and possibly a deck, etc) and they record the shows for you. I think you might find more than a few people at TS.com who would be happy to do that for you...especially if you can smooth the way for them.