Yes, you can! The ADS7-V2EBZ has a trigger connector (J5) to act as a trigger input. The attached document explains how the trigger mode can be used for AD9695 evaluation board on ADS7-V2EBZ. The same technique can be used for capturing data from AD9208 and AD9689 evaluation boards.
Note : Not all FPGA bin files and ADC/DAC products support this mode. So please check with the appropriate applications support personnel before trying out this option.