When I soft proof a black and white image using the ICC profile for Juniper Baryta Rag I am seeing a slightly warm image, which I actually like very much. If I print on an Epson p700 in the ABW mode using the neutral setting, will I see this slightly warm tone of the paper? I know I can select the warm tone in the ABW mode. Will this warm tone be on top of the natural warm tone of the paper?

I can not just test for this since I do not yet own an Epson p700 and I am still waiting for the p700 to start shipping again.

When soft proofing you're likely seeing a warmer image because you have the paper white simulation selected. To approximate the base color of the paper your software reads the paper white point from the ICC profile and tints the image. While it is not 100% accurate, it does give you an idea of how the base color may influence the print.

The warm tone in Epson's ABW acts similar to sepia toner, and warms up the printed image. This will be in addition to the base color of the paper, so I would recommend starting at the 'neutral' setting in ABW for your first test print (unless you're specifically looking for a sepia print).

Hope your printer ships soon!