1AWG with a smaller breaker?
Sure, you can always upsize the wire.   

However, a dramatic upsize introduces two complications. 


the much-larger wire will not fit on the device.  It will need to be pigtailed to a suitably sized wire, such as a 6 AWG.  


When dealing with #1 wire, it's not as simple as using a giant orange wire-nut the size of a salt shaker.  You have to use a connector such as a Polaris, which is an insulated lug terminal.   You could also use uninsulated lug terminals or split bolts, if you don't mind lashing it under unbelievable amounts of electrical tape.  You do need to insulate neutrals.  


You are probably dealing with aluminum wire (I hope)


Generally all terminations sized for #1 wire are aluminum friendly; why wouldn't they, since aluminum is normal and expected at these sizes.  You just have to take care to use terminations rated for aluminum; a Polaris is fine, however I would not use a split bolt unless the smaller wire is also aluminum. Aluminum is fine to use at these sizes.  

But yes, definitely lay the heavier wire.  The only case where I wouldn't is if the wire was in conduit, and the run is very short.  In that case, the pigtail adapters for the larger wire might be more expensive than just doing the whole run in the smaller wire.  It could be changed for the larger wire later.