What are the drawbacks of transmitting RF frequencies through an antenna that is designed for different frequency?
Part of your output power will be ultimately wasted as heat in the antenna,
feedline, matching elements, transmitter etc. (less range)
Energy will "bounce back" from the antenna to your transceiver. May potentially damage it.
Energy "bounced" from the antenna may cause intermodulation distortion in your transmitter. The transmitter will become a poor mixer (the device may not be compliant/legal, may transmit undesired frequencies).
When receiving (if the same antenna is used for RX/TX) you will "hear" other frequencies better than the one you are using for communication (worse sensitivity, higher noise level).