Neither program can use the other's database, but both programs can read and write metadata to the same location, meaning that the two programs can work together without stepping on each other. That said, Lightroom takes an extra push to read metadata that other programs have changed (you need to manually tell it, in one of a few ways, that you actually want those changes and not the version of the metadata as it exists in the Lightroom Catalog).
Do PM+ users delete the images from the LR catalog after edits?
You could do that, but at that point you might as well just delete the Catalog and start a new one for the next project (although I think the option for Lightroom to write changes into XMP is a per-catalog setting, so you'd probably want to make sure to change that if there is no way to set that as a default). Or you could just import the things that you need to edit into a Lightroom Library strictly for editing, and not worry to much about whether not something is in a Lightroom Catalog or not.
I have been thinking of upgrading to PM+, and like a dummy didn't play with it when I had a trial period.
I am sure we can help if you would like to try Photo Mechanic Plus's capabilities if you send an email to support@camerabits.com