It is always iffy to provide generic answers to generic questions without any data to back up statements.
If a mismatched antenna still works, depends on the system specifications (antenna and transmitter/receiver).

For the referenced antenna at http://www.air-store.eu/GAV-868 there is no data at all.
It is impossible to know how that antenna, intended for 868MHz, performs at 916MHz without evaluating the frequency characteristic of that antenna.

The antenna referenced by Bumper has some data.
The specified VSWR of 1.2 at 1030 to 1090 MHZ looks very good.
But you need to know the VSWR at 916MHz.
If that is still at 1.5 or so, it is still a good antenna for US Flarm.
If the VSWR at 916MHz increases beyond 2 it becomes questionable.
This means that more of the RF energy from the transmitter is being reflected by the antenna back into the transmitter (instead of radiated out) which will heat up the transmitter and might damage it.
It looks aerodynamically very sleek but I am not a aerodynamicist.
These antennas are monopoles, which means that they need a groundplane.
No big deal. You just need to know and take care of it by having foil / sheet metal / mesh underneath (e.g. aluminum roof flashing)

Antennas are reciprocal devices. With respect to performance, you will notice the same degradation effects of mismatch for receive as for transmit.
As mentioned above, the danger of mismatch at the transmit side is the reflection of energy back from the antenna into the transmitter, potentially damaging the transmit power amplifier. That is not an issue at the receive side.

3U