You don't strictly need GTM to run a lead form campaign, but the answer really depends on where your lead form lives.
If you're using Google Ads lead form extensions (the ones hosted inside the ad itself), GTM is irrelevant - Google handles that tracking natively inside the platform. No issues there.
But if you're sending traffic to a landing page with a form on your own site, GTM makes life dramatically easier. Yes, you can hardcode the Google Ads conversion tag directly onto the thank-you page or fire it via a form submission event, but that's brittle. Every time you need to add a new conversion action - a phone click, WhatsApp click, GA4 event, maybe a HubSpot form submission - you're back in the source code.
With GTM, you set up the conversion linker, a form submission trigger (or a custom HTML listener), and you're done. You can add GA4 events, multiple conversion tags, and even Facebook CAPI all from one container without ever touching the site code again.
My take: the campaign can run without GTM, but clean tracking is what makes Google Ads optimise properly. Bad conversion data means the algorithm learns the wrong patterns. I'd always set up GTM from day one - it's a few extra minutes that saves hours of debugging later.