You sound right.
The impulse modulation description of ideal sampling operation introduces an amplitude scale of $1/T$ on the spectrum of the sampled signal, which is a periodic replica of the original spectrum.
Note that as the sampling period $T$ gets shorter, the scale factor gets larger and the separation between repeating replicas gets wider too.
This is an ideal operation. In practice, what you are interested in is the finite valued samples of the signal at the sampling instants; the sample values (envelope) will be the same irrespective of the sampling period.