Sure if you are out in the open, you can get a signals variety shot in only 5 seconds or so. That means 2 of them would only take 10 seconds of actual time for the gps to determine it's position over 2 separate spots.
It might take a full minute or more if you are in shrouded woods with overhead canopy, which will interfere with the gps signals coming from space. The speed of light is so fast, that even 1 nanosecond of timing error is equal to 1 foot of distance error. That's why sometimes a nanosecond is also called a "Light Foot".
It is also a good idea to put in your point description the compass reading for where the 2 circles will intersect, so you know which one to hold. Because when you do a distance, distance intersection in autocad, the circles will intersect twice, and you want to make sure to pick the correct one otherwise the created point will be very wrong lol.
I've used this technique a few times on pesky boundary corner monuments that are literally set in the middle of the base of a grown tree, and you can't get the gps receiver up on it naturally, not plumb at least.
If you use the tilt compensation with the Javad system, I believe it uses the internal compass for providing the corrections, it does not have a full and true Inertial Measurement Unit (IMU), unfortunately. So that's another reason why you would want to use the distance, distance intersection option.
Although, the horizontal distance, distance technique doesn't work for vertical, bummer.