Combination of both.
I think your off-road enjoyment will be hampered by concerns for the shiny new £9k bike unless you're only planning on taking it on some really light trails, in which case you could use the GSA. If you do get the off-road bug, experience from friends and on this forum suggests you'll be looking for something cheaper and lighter soon enough. At which point you'll be back to square one with regards to balancing having to do 100+ miles on road to get to the trails vs. the inconvenience of a trailer or van to get a more suitable off road bike to them.
All of the above is based on my own thinking given that I live near you so appreciate the dearth of any trails (decent or otherwise) near us and the fact I've been through this thought process myself a while ago after me and a few mates did some off-road experiences and wanted more. In the end we ended up just cherry picking a bunch of off-road experiences with bike hire (I can highly recommend you give trials riding a go).
At the end of the day I think the AT is a cracking bike and I hope you get everything out of it that you're looking for. As I said I was close to picking one up too simply because that deal was so good, but that doesn't mean it'll make a good first off-road bike.