After receiving this question I thought why not just trying it out within a hands-on video. I didn’t had tested this beforehand, so let’s see:
If you didn’t watch the video before reading further this would be the spoiler section of the post.
The Nissin Di622 will not be triggered by a random studio strobe but it works the other way around. You could also use the pop-up flash of your camera to trigger the studio strobe is you don’t have a radiographic trigger (recommended).
The disadvantage would be that the pop-up flash and/or the Nissin would have influence on the image even if you don’t want this to happen.
Some camera’s however have a control mode for the pop-up flash so that it’s powered down a lot with the only purpose to trigger an external flash without influencing the image.
Have a nice day shooting!