I think the short answer is "no" if you are doing a direct lightroom merge to HDR. You can use an edit-in and choose "merge .. in Photoshop" and do the merge there, and from Photoshop you can save-as, though this is not quite the same thing as letting LR do it.

I think the more broad answer is having the drive/folder as read-only is not compatible with a number of lightroom features. When you edit in an external program (most plugins, or even photoshop) the normal behavior is to export a file (usually a TIFF) into the same folder as the original image, and operate on that file. Subsequent edits are usually done by editing that same TIFF (or occasionally producing yet another one). And clearly direct modification such as convert to DNG requires write access, as does writing metadata (for some file types), and updating capture date/time.

While it is perfectly true that Lightroom is "non-destructive" and so should not need to write to the original file for most usage, many of its features assume it can write to the folder on which the file resides, and a very few to the file itself. While there are some workarounds, it may be worth asking if you can put the protections at a file, not folder level, to protect your originals.