On the one hand, it seems obvious that they would, to ensure that the digitisation worked. On the other hand, they’d probably get through 1 customer per month if they did that. So either they just dump the material to a file and send it, or they check every 10 minutes or so and watch a few seconds, but no more than that. Does that sound about right? 🤔
I have some stuff from 30+ years ago I’d like digitised, but I don’t know how I feel about a stranger watching 9-year old me be disproportionately excited to the point of tears about my Christmas gift of a life-size cardboard cutout of Wesley Snipes that my dad almost certainly stole from the video rental store. Some memories should stay memories.


You might check around with your friends and relatives, to see if any of them digitize stuff; I’ve done it on a casual basis for some of my friends and relatives.
Alternatively, you can probably get an old VHS machine at Goodwill, give it a quick cleaning, and pick up various digitizers (standalone recorder or computer-input) and convert your own tapes. If you do it yourself, I would strongly suggest checking your setup with old commercial tapes first, so that you iron out any setup issues on something you don’t care about, before sending your irreplaceable tapes through whatever process you have.
[Note on commercial tapes: some of them have copyright protection on them, which will make the video fine when you send it to a tv, but just make it erratic when you send the video through another device. Very very occasionally, for undetermined reasons, an entirely home-recorded tape will also exhibit this behavior. If this happens to you, there are two main options: (1) if the device you’re recording onto has front input jacks, switch your setup to record through those jacks, as many of the front inputs lack the monitoring needed to screw up your recordings. (2) Check eBay or other online shopping places for a “video stabilizer”, which is old-timey code for “copyright buster”. Look at the listing for some indication that it’s used for VHS or VCR.]
If you think there might be issues with the tape quality (for example, dropouts or the magnetized bits sticking to the back of the previous strip on the reel), you might want to go professional - but only after seeing what steps they take to minimize this, and what that might cost.
Edit: when I did this for family and friends, I’d monitor the first five minutes or so of each recording, simply to make sure that the tape wasn’t crinkling (more likely to happen at the start of a tape, or some midpoint that was heavily used (repeatedly rewatching a single scene) of where someone had left the tape sitting. And then I’d check in periodically, to see if the tracking needed to be adjusted. I’d also try to at least stay in the same room, so that I could react quickly if I heard the tape crinkling.
Also, in an attempt to minimize problems with the tape having become slack over the years (even if properly stored on their spines), before I started any new tape, I would: if it was stopped partway or at the end of the reel, I would rewind the tape to the start, fastforward it to the end, then rewind it again, to try to reset the tension on the tape. If the tape was stopped at the start of the reel, I’d fastforward and then rewind, to reset the tension.
Also, if you do this yourself, it’s good to have some old tapes lying about that you don’t care about, either old commercial tapes or home-recorded tapes with content you don’t care about. This is because every so often, a tape will jam inside it’s cassette, at which point you need to open it up and unjam it. But sometimes the cassette itself (but not the tape) has developed problems, and you need to re-shell the tape into the shell of a different cassette.