DickH said:
The power supply will overheat and may eventually burn out, unless it starts a fire before then. Let's hope you are there when that happens !
7 AMPS? What is it, a 500 watt transmitter?
1) 7A at 12V is 84W, with an efficiency between .25 and .75 that could be about a 20 to 65 watt radio.
2) More likely than burning out the power supply you will either blow the fuse, or the voltage will sag.
3) No one said what type of transmitter, if it is AM or SSB, then you will only have sag problems during modulation peaks which will most likely distort the signal.
4) Some poorly designed power supplies will put out hum when they are overloaded, again distorting the signal.
More information is needed to get good answers.
Remember,
always put as much though into your question as you want in the answer.