Can I use a RFID reader to check if there is an physical obstacle between it and the tag?
A main problem with RFID is the power transmitted by the reader module to the tag. With some on-PCB designs, such as Texas Instruments proposes through an evaluation kit for the 7960A, you can support a reading range up to 4 cm, where ID Innovations will propose a all-in-case reader up to 12 cm. Unfortunately, human body is larger than these metrics.

You can still get readers with a better range, but this is really not the same price I swear.

A cheap alternative could be the usage of a modulated IR signal as a fence. It just needs a MAX555 to modulate and power the IR diode signal on the emitter side, and a photo-transistor plus an analog comparator on the receiver. You add a peak-detector (diode + RC dipole) at the output in order to get major changes (i.e: your signal will go down only when somebody is seated, not due to the signal reconstitution) and it could sound good. You can get it for less than $8 I suppose.