My question is in regards to pushing values to either Picklist fields or Multi-select Picklist fields through a CSV upload or API.

Do the values you push need to match exactly the selectable values you've setup within these fields, or can you push other values not present as selectable values within the CRM itself? (I recall in SFDC, we could push whatever values we wanted to a Picklist field during CSV uploads or API record syncs despite whatever choices we had setup in the CRM UI as selectable.)