Hello;
Everytime you correlate any DAQ operation with a Software call in Labview or any other programming language, you will not get a hardware precision on that operation. Then you can expect a delay of a couple of miliseconds if you are using Software calls together with DAQ. Regarding your second question, if the signal you are intending to detect is TTL, you can use one of the general purpose counters of that equipment of your, to monitor the counter value. Then, when the counter has a value different from zero at its register value, that means the trigger already happened.
Hope this helps.
Filipe