Can an Army Reserve unit block my transfer to another unit?

Yes they can block it....per say. The Commander is not required to approve the transfer request. If the Commander for your current unit needs you in that slot, then you will be staying put. I forgot to add that your transfer request, when submitted, still needs to run thru ALL the channels it is supposed to run thru. It doesn't stop at your unit Commander's desk. Or rather, it's not supposed to stop there.

Take a look at AR 140-10.
Your unit is not the approval/disapproval level for this kind of transfer.
And a deployment two years from now is not a good enough excuse.
A deployment less than six months from now might be,

Normally this is not a problem as Reservists do this all the time. And most commands are reciprocal as transfers flow in both directions.

They can, but like everyone else said the packet should go forward and I would make sure it does ,ask them to Cc you in the emails and let them Know you want to know the status .If you are in your IRR window you can go Irr and they can’t stop that , but get a hold of your current retention NOC0 79V and have them help you if you unit isn’t helping

Most units let you transfer when you move that far away, not sure why they would want to block someone, plus 2 years out is plenty of time to get a replacement, hell I was cross leveled out of my unit in 2014 and sent 5 hours away to another unit because when they came down on orders all those who could retire, dropped packets and got out.

Yes they can but any good commander would let you transfer out if you live that far from the unit.