Maybe. HDR monitors are typically going to be some approximation of the DCI-P3 color space, while Adobe's wide-color rendering is the Adobe RGB color space. The two are similar but not quite the same; in particular, Adobe RGB extends a bit further into the green-cyan range than DCI-P3 does:
That said, these are only idealized color spaces, and the gamut of a given actual monitor is going to differ somewhat from these. That's why you'll see monitors advertised as having "99% Adobe RGB coverage" or "99% DCI-P3" or some such.
So, a typical HDR monitor can probably reproduce most of the Adobe space but maybe not quite all of it, but in practice it might be just about as good as an actual Adobe-supporting monitor.
That said, I don't know whether Photoshop and the drivers/OS/etc will actually cooperate to let you turn on Adobe RGB rendering on a DCI-P3 HDR monitor. If Photoshop is outputting 10-bit color in Adobe RGB space, but the monitor doesn't actually take that format, then it would need to be converted somewhere along the line to a color space and encoding that the monitor can take as input. That can certainly be done by the graphics card/drivers/OS, but I don't know whether the support for doing such conversions is actually there.