Yes. During a standby period any duty may be assigned (ORO.FTL.105 (25)). That includes airport standby or duty at the airport.
Limits for assignment of airport standby after home standby are not explicitly mentioned in CS FTL.1.225.
The assignment of airport standby is considered as airport duty and the subsequent FDP counts from the airport reporting time as stated in ORO.FTL.225 (d).
If the other-standby lasts less than 6 hours, the maximum FDP counts from reporting for the airport standby. If the other-standby lasts more than 6 hours, a reduction is applicable to the subsequent FDP.
If an FDP is assigned during the airport standby, the combination of home standby and FDP does not lead to more than 18 hours awake time.