Jody, yes it is workable.  In fact, I do it all the time.

Any image I consider important makes a trip to Photoshop for refining and local adjustments.  If I am just banging out proofs for a client, or if I want to email some quick pics to friends, I don't bother going to Photoshop at all. I just get it close in LR.

For those important prints, I use LR to get my global settings close, such as color balance, tint, black points, white points, contrast, etc.  But if it is going to Photoshop for further work, I always leave plenty of headroom.  For example, I don't push the white and black points to their endpoints, I use little or no Saturation boost, minimal sharpening, etc.  Once in Photoshop, I have much more control and can adjust local areas as I wish.  I can also soft proof the image and get it just right for print.  I usually print directly from Photoshop while I am there, at least large prints.

When you save the image from Photoshop as a TIFF, PSD or JPG, the changes will be locked in and LR will display the image pretty accurately.  All the slider controls will be set to zero, since you now have a new file (slider positions on your original raw images will remain where they were when you exported it to Photoshop).  Then, if you wish to print from LR, just use the same color profile, paper, rendering intent, etc, and the print should look the same as a print from Photoshop (assuming the same profile, intent, paper, etc).

I have no experience with MPIX or WHCC.  Many years ago, I downloaded a Costco profile from Dry Creek Photo (http://www.drycreekphoto.com/) and used it to soft proof my image for a specific Costco store.  This was for a Fuji Frontier printer, and it worked quite well.  I have no idea how current these profiles are or how consistent local labs are with their calibration or handling of files. Many Labs are a moving target, in my experience.

Lou