I am imagining a scenario in which a user is checked into a venue by taking action with a particular device.
The most common scenario would be a gym/fitness center where a patron would scan an ID card or badge up entering.
Is it allowable to use the foursquare API to check into a venue as such after a user has granted access via oAuth?
Yep!
There are many apps that check people into foursquare using the API. (Including the official foursquare clients, Gowalla (RIP), venmo, foodspotting, and plenty of others).
Your scenario sounds ideal for check-in integration as you have a good sense of location (in this exact gym), and it's an explicit action on the part of the user that starts the check-in process (using a RFID card on machine X).
Just be sure not to abuse the power, because the user will see these check-ins in their timeline. It would probably be good to have a clear policy on the default privacy settings for them (eg - always private).