Completely new to GrowthBook - is there usually a long delay in the script tag connection? As currently, it's just saying that the SDK connection is 'Not connected' despite me adding this in Tag Manager

No, there shouldn't be a long delay. Using GTM always includes certain quirks. Did you see our guide on setting up GrowthBook with GTM? https://docs.growthbook.io/guide/google-tag-manager-and-growthbook