No. While the X1R-C and XPro-S are compatible in terms of firing and possibly M power control, the Godox X1R receivers do not perform cross-brand TTL in the way the built-in radio transceivers in the Godox TTL full-sized speedlights (TT685, V860II, V1) do.

If, say, you were to purchase a Godox TT685-C and checked its firmware version was v3.1 or later, you could use it off-camera as a radio slave in TTL with the XPro-S. I use one that way with an XPro‑C on my 5DMkII, my XPro-F on my Fuji X100T, and my Xpro-O on my Panasonic GX7.

Obviously, however, trading in your 600EX-RT for a TT685-S, V860II-S, or V1-S, if you've moved completely to Sony would make more sense, so you could have a speedlight that did TTL/HSS on-camera as well as off-camera. Keep in mind, there is a known bug with Godox and Sony that TTL underexposes if used with wider-than-f/4 aperture settings. So, sticking with M and using, say, super-cheap $65 TT600 or TT600S single-pin manual speedlights may be another option to consider.

Alternatively, don't use Godox as your triggering system. Cactus's V6II transceivers can do cross-brand TTL in their X-TTL system.