Both Tate and Tveit must be very busy with their schedule (I mean, Tate will leave the show a month before its end!) so it's unlikely to think they will stay with Assassins any longer. And it would be incredibly strange if they open in West End just a couple of weeks after closing at Menier, there wouldn't be any time to advertise it properly. Also, no West End theatre can accommodated Assassins as it's currently designed at Menier, they should make a lot of changing with scenery and direction...
I love Sondheim and I'm fond of this show (I've seen four different productions), but I can't for the life of me see this doing any sort of business in the West End.