Does 2Do support syncing with Exchange?

No. 2Do currently supports syncing with iCloud, Dropbox, Apple Reminders, Todoist, Toodledo, and CalDAV servers (such as iCloud CalDAV, Fastmail, Fruux, Yahoo!, Nextcloud, SabreDAV, and so on). Exchange is not one of them. See Which sync method should I use? or the Sync overview (Mac) for the full list.

Adding an Exchange account to your Mac or iOS Calendar app can make its events visible in 2Do's calendar views, including the Calendar Events view on iPhone and iPad and the Calendar Events day bar above the Today list on Mac. It does not enable Exchange task synchronization in 2Do.