Yes, there is measurable delay, but on many cameras it’s only on the order of a few dozen milliseconds overall. Typical shutter-lag figures published for interchangeable-lens cameras are roughly 22–53 ms, with many pro DSLRs around 36–49 ms. That total includes the mechanical sequence needed to make the exposure, such as mirror movement and shutter actuation.

For water-drop photography, that amount of delay can matter if you’re trying to trigger at an exact instant. Using mirror lock-up and/or holding the shutter open in bulb mode can reduce the camera-timing uncertainty, leaving the flash timing as the main event that freezes the motion.

So: your process can be worth it when precision matters. If your setup depends on repeatable millisecond timing, pre-raising the mirror and opening the shutter first is a reasonable way to minimize lag from the camera body.