For someone without too much stuff, who isn't in a huge hurry, and when the weather isn't too bad - yes! It'll add 10-15 minutes to your journey, however, and involves about 100m of walking with no footpath.
From the airport, take the exit for the tram and buses, then keep walking past the trams towards the Hilton Airport hotel. Go past the hire car centre, and take the road that's nearly straight on (Eastfield Road) past the front of the hotel and continue. When you reach the entrance to the Ingliston Park & Ride, turn left in, walk up the entrance road (no footpath here), then cross the grass into the carpark as soon as you can. Keep going straight on following the signs to reach the tram.
From the city, get off at the last "normal" stop at Ingliston Park & Ride. Go out into the carpark, then keep going, to the right of the bus waiting area structure. Go past the sign saying "no pedestrian access to the airport", walk over a meter of grass, and then walk ~100m along the access road (no footpath). Turn right at the main road, and walk along the footpath towards the Hilton Airport hotel. Past the Hilton, go straight on past the hire car area, then follow the footpath slightly to the right up to the tram & bus stop, then the airport itself.
From the tram stop, it takes about 5 minutes to walk to the Hilton. It's about 10 minutes from the Hilton on to the P&R.