No you have to go to the Develop module, and click the Soft Proof option (I think it's a tick box, but don't have LR in front of me at the moment). This brings up the Soft proofing tools at the top of the right hand tool panel. You need to select the correct .icc profile here, remembering that the same paper has different profiles on different printers. By default I think it starts with sRGB as your profile. If you click in the profile box you can select from a list of profiles, including one selection that allows you to add additional profiles to the list. You will need to find the correct profile to match both the printer and paper combination. For printing I also always use the simulate paper white, although not perfect it is quite good at matching the brightness/contrast of the final print, although you do need to still have the screen brightness set correctly. Once you have chosen the correct profile if you then start to edit the image, to correct for any differences that show up, such as the skin tones in your case, LR will ask if you want to make a Proof copy, accept the proof copy and it will create a VC for you. I usually use a Blue label for Proof VC's to make them easy to find. Once you have the proof copy looking good, then you can take it to the Print module and print it. At this point you should find that the Print module will use the correct .icc profile automatically.
The reason that LR does it this way is that you need to be in the Develop module when Proofing, so that you can make any necessary edits to the proof copy to make the image correctly fit the different available colourspaces. Instead of showing under or over exposure the two warning triangles (although they get different icons) in the corners of the histogram show Gamut warnings. One for the monitor, the other for the printer colourspaces, and the highlighting will combine and show purple if any part of the image is out of gamut for both.
In my normal processing workflow I will usually soft proof, and create a Proof copy for my usual printing choice, for any image that I think might be a good choice for printing. It doesn't normally take long, and I have the thing ready to go if I want it. My usual choice for a print is from a lab, so having images ready to go is useful if I have something I really want printed, as I can then quickly find images that are ready to add to the order, to help offset the postage costs. Much easier to have a couple of dozen low priority images on hand when I want to print something important.
Alan