Unfortunately not. Airtable’s field types are either reactive (i.e. pulling data from somewhere else: formula, rollup, lookup, etc), or manual entry (single/multiple select, single line text, date, etc.). They can’t be both.
You can add a new entry to that multiple select field on the fly, though not while in a form view. You’ll have to do it in the expanded record in a grid or other non-form view. Tap on the field in the expanded record, and you’ll see something like this:
In the field that says “Find or add option,” type the name of the option you want to add, then tap the button starting with the label “New” that shows your new item.