Yes, I think that would work
The Escape is Altus 8 speed with rim brakes. For a 10 speed replacement group you will not need to mess with the hub, a 10 speed cassette will fit
The bottom bracket shell is threaded as the Escape has a cartridge BB. You'll obviously need to replace that with a external bearing unit. It does not matter if the shell is 68 or 73mm width.
The rear spacing is going to be 135mm. A Deore crank compatible with a 68 or 73mm threaded bottom bracket shell will have an acceptable chainline.