I select some pictures in Lightroom and then choose Edit In -> Photoshop HDR Pro. If I choose 32 Bit, there is an option box for "Complete Toning in Adobe Camera Raw". If I do NOT check this box, am I losing something? That is, if I want to do all of the exposure adjustment, etc. in Lightroom, then can I just click "OK" with "Complete Toning in Adobe Camera Raw" unchecked?
No, not at all. This is the correct method for creating 32 bit images to edit in Lightroom. Just convert to 32 bit - leave Complete toning in ACR Unchecked and save the resulting 32 bit Tiff back into Lightroom