No, the Mychron is not a transmitter for the AMB Timing and Scoring system.
Yes, buy your own transponder if you race on a regular basis.
As far as I know the only transponder you can buy is a proprietary device from AMB.
Here is a dealer…https://www.pegasusautoracing.com/productdetails.asp?RecID=6656
Look around and you can find the used for a lot less.
Steve O’Hara