Yes, RME in LMS will upgrade the entire stack at once as if it were one device. To upgrade a device, go to RME > Software Management > Software Distribution, and create a new deployment job. If you do not already have the desired image in your repository, go to RME > Software Management > Software Repository, and add the new image.
Some caveats with using RME to upgrade the stack are it cannot handle a mixed stack. That is, if you have both 3750s and 3750-E switches in the same stack, RME will not be able to upgrade the stack.
Also, RME will use the /overwrite flag when copying the new image to flash. If your master switch does not have enough space in flash, RME will clean up the flash so space for the new image is available. The member switches will not be cleaned up. So, if you have other images in flash (other than the main 12.2(35)SE image), then you will have to manually delete those files prior to running the SWIM job from RME.