Yes. My work implemented this a few months back. Now any site that detects ad blockers detects this too and you can't turn it off for just that site. So this is more annoying and cumbersome than a browser level ad blocker that you can turn off on specific sites.
Most modern sites have scripts that check if the ad successfully loaded. Short of modding the code on the html page to remove the check, you can't bypass these by simply avoiding the ad load no matter at what point you prevent it from loading.
The PiHole blocks ads at the network level, when it sees your computer ask for an ad, it doesn't forward the request. Browser-based blockers sometimes do this too, but usually, they check ads by examining the properties after your computer has received it, but before you see it.
PiHole is harder for websites to detect. If the DNS server or ad server had issues, it would look the same to the website. I haven't ever seen an "ad-blocker" detected when I have PiHole on, but my browser blocker off. P.S. Disabling javascript will often block the script that checks for ad-blockers. There are extensions that put a switch next to the URL bar, and you just click it if you want to try with javascript disabled.
I ran Pi-Hole for a bit but ran into some sites that it broke - it wasn't worth the hassle to sort it all out so I went back to normal ad blocker plugins. The nice thing about it though is it also blocks ads on smart TVs/etc that are on your network.
I do occasionally run into this. You can manually add websites to the allowlist, which is admittedly a pain. You can also go to pihole admin and just turn PiHole off for five minutes, and it can turn itself back on again. It's two clicks and takes 30 seconds.
@frugalnacho I'm using a Pi Zero W as well. My Pi also sets next to the router. I eventually added the ethernet adapter. I was experiencing network issues, and after the adapter, the issues went away. I'm not convinced it was the adapter, and I'm sure it's dependent on the router.