You are wrong! Sometimes. You can detect "it" by looking at the vowel just before the stop closure. This paper may be useful (there are pictures). Compare the non-glottalized non-creaky example with the 3 examples with glottalization and/or creakiness, and notice the wide spacing of the glottal pulses in the latter trio. For a more expanded / extended view of laryngeal things, consult Esling et al. Voice Quality: The Laryngeal Articulator Model which is very useful in pointing out the diverse range of things called "creaky" or "glottalized". Mow, saying that there is an "accompanying glottal stop" suggests you mean either phonological [hɪʔt] or [hɪtʔ], where /t/ actually phonologically splits into two distinct segments. If so, you'd have to spell out your theory of phonology and your theory of phonetics. Generally, phonologists at most claim that the stop becomes "glottalized" ([+constricted glottis]), without saying that it becomes two segments, and we leave it to the phonetics to describe the time course of the glottalization.
It might be useful to consider what it would mean for "t" and "ʔ" to be simultaneous. Nothing happens instantaneously in speech; phonological "t" relates to a complex package of events over time. Thus there are formant transitions on the vowel before t, because the tongue starts to move towards a target position while the vowel is still being produced. One convention in dividing up continuous speech is that you look for the "closure" defining a stop, but there is interesting stuff happening milliseconds before you get the actual closure. The larynx is kind of slow, and "glottal stops" start kind of early compared to e.g. alveolars. Therefore the idea that a glottal stop and an alveolar stop (starting with the closure) would occupy exactly the same moments of time is unlikely. They will overlap substantially, but not crisply / precisely.