There's a duplicate question (https://www.odoo.com/forum/help-1/question/mass-mailing-howto-v7-5825) but no one seems to answer there anymore.
Mass Mailing in v7 sends mail only to the followers of selected partners, not to the partners themselves. According to Fabien Pinckaers (fp) this was solved more than a year ago but it actually never was. Looking at the source code of the current trunk (v8) it was fixed but never for v7. Can we expect a fix or will this only be available in v8?
This seems an important point to verify.
Have you checked the v7 saas branches. It may have been fixed in a one of those branches and not in 7.0.
There seem to have been changes related to mass mailing in saas-5 branch. Is that v7? I couldn't find any information on those branches online.