Is HDR mode editing useful for SDR output?

The simplest answer is that the new HDR mode is only beneficial when using an HDR-capable monitor (which is now very common - the vast majority of smartphones, Apple laptops, TVs, etc): https://gregbenzphotography.com/hdr/

Beyond intentional sharing of an HDR edit, working in HDR mode has a few benefits even for your SDR work:

• It is much easier to adjust white balance correctly in HDR mode as mistakes are more obvious (so enable HDR, set white blance, and turn off HDR for a better SDR result).
• It is very helpful from a learning perspective as you can see the actual data in your RAW file. The common myth about "recovering highlights" is much easier to understand when you view the RAW image on a display that shows you what's actually in the RAW.

I would encourage spending some time with HDR to understand it, even if you believe you have no immediate use for it. You will need a supporting display, and Apple laptops, iPhone, Pixel Pro, and the M4 iPad Pro are all great ways to see HDR in Lightroom now (there are many other HDR-capable displays, just mentioning the most common ones).

all of my work is targeted towards print…Is there any benefit to editing HDR files in HDR? Or is all of that information already compressed into the SDR range when I'm editing in SDR mode?

By @David Adam Edelstein

For images that will only ever be printed, I don’t think HDR editing is a good use of time given that HDR can’t be reproduced in print. If you’re all about printing, you’ll probably still edit your “HDR merged” images, and other images, for SDR. If you edit with HDR switched off (the default), the information isn’t compressed, it’s as it always was and as you’re used to. Enabling HDR would extend the tonal range, with your ability to preview it depending on how far your display extends into HDR.

If you did edit with HDR enabled, and you want an optimal SDR conversion (for print or for SDR displays), you should also be adjusting the SDR Rendition Settings. Because one of the major problems with HDR on SDR is that there is no automatic way to reliably make all HDR images look good when their tonal range is compressed down to SDR. It’s a reason there are multiple HDR-to-SDR standards for HDR video. 

If you adjust the SDR Rendition Settings in Lightroom Classic or Camera Raw, now you are taking control of the HDR-to-SDR conversion, manually tuning it for that specific image. This should look better than an automatic conversion. SDR Rendition Settings are a way that Adobe lets you store adjustments customized for both HDR and SDR in a single instance of the image.

Editing for print is still one step beyond an edit for an SDR display, as it always has been. If you normally find value in soft-proofing, that will still be valuable for tuning the image for your specific combination of printer, ink, and paper. So if you edited in HDR, and also tuned the SDR Rendition Settings, you would still probably want to preview that by soft-proofing through the print profile. Although the SDR Rendition Settings do have a Preview for SDR Display option, that is still at the display level, not using any print profile, so it isn’t a substitute for print soft-proofing.

Personally, for prints that have to look their best, regardless of whether I edit an image in HDR or SDR, I’ll probably continue branching off an SDR proof copy (virtual copy of a soft proof) with adjustments customized for the specific print specs.

All of that information is still used and just compressed into SDR range when in SDR mode. The exact compression method in the traditional SDR mode is slightly different from the SDR downconversion when in HDR mode, so you might find one is subtly different from the other. Also, the tone curve module (specifically the point curve) works a bit differently in HDR mode which might be useful to you. Outside of those two things, there is no difference when delivering for SDR monitors or print. HDR mode mainly exists for delivering images for HDR screens.

My understanding is that you need to have HDR displays or there is no visible benefit in using the HDR mode.   

https://helpx.adobe.com/lightroom-classic/help/hdr-output.html