The English practice of turning a /t/ into a glottal stop /ʔ/ does not happen like that in German. In German, a glottal stop is only an unwritten consonant that occurs between words if otherwise two identical vowels would meet. Thus, ja, aber is pronounced /jaʔˈabɐ/ (the -er of aber can be rendered differently) with a glottal stop.
However, German colloquial speech does feature the weakening of alveolar stops (/t/ and /d/) before syllabic nasals. Rather than turning it into a glottal stop, the alveolar stop and the syllabic merge to something between a /d/ and an /n/. This can be more or less pronounced depending on whether the person in question speaks dialect, which dialect they speak and which part of the German speaking countries they come from. Bavarian is especially known for merging those two consonant sounds into one, in my opinion.
Now if you do use the English glottalisation, you will still probably be understood (/ʔn/ is similar to what Germans make out of it) but it would still have some kind of a weird ‘ring’ to it — at least it had to my ears when I just attempted to pronounce a word like Latten using the English t-glottalisation.