Google Tag Manager (googletagmanager.com) does not load trackers itself, it manages them. The actual data-protection issue is the tags it deploys.
If the Tag Manager loads consent-requiring tags (Analytics, Ads, Pixel) before or despite a rejection, there is no legal basis for these under § 25 (1) TDDDG. The container request itself already transmits the IP to Google (USA).
The free scan checks the delivered HTML and shows which services are embedded, whether a cookie banner is detected and whether privacy-policy and legal-notice links are present — with context for each finding. It is not a substitute for legal advice.
This text is general information to the best of our knowledge, not legal advice. For an individual case, consult a law firm specialising in IT law.