The digital counter inputs are TTL level, so the high level (triggered) will be about 2.5 volts. I wouldn't suggest doing this, however, without an interface to the counter input from your signal.
A good choice would be to use a comparator. Put a reference voltage you want to switch at on the (-)input (you can use another DAC output as the reference to make it fully adjustable at any time), and the output signal you want to trigger from on the (+)input. The output of the comparator will be one of two states, equal to the power supply voltages (+/-12V usually). You can then take that output to another buffer stage- there are many xxx-to-TTL buffer ICs available.