According to the Intel® Edison Product Brief Edison only supports 802.11 a/b/g/n. But since the main difference between the 802.11 a and the 802.11 p standards is that the latter divides its frequency to 10MHz (theoretically half the bandwidth of 802.11 a), I believe it might be possible, however it will require to modify the BCM43340's driver. The BCM43340's driver can be found in 01org/edison-bcm43340 · GitHub, nevertheless it is provided to us by Broadcom, so if you wish to modify it to enable 802.11 p support, my best suggestion is that you contact Broadcom.
thank you for your fast and informative answer.
I sent a mail to the Broadcom linux driver support, which was the only email address I found so I hope to get there an answer.
I'm not so familiar with linux driver so I don't think that I could modify the actual one.
Hopefully there will be a solution since the Edison would be the perfect platform for this project.