Basically, yes. Oh, you might luck out and find a pre-amp bordering on harsh that makes a mic bordering on woolly sound superficially better but that would be luck of a draw.
Basically, the pre-amp's job is to take the mic signal which starts off around -50 or -60dBu and amplifies it to around 0dBu. The designers try to do this with as little added noise and as little change to frequency response as possible. However, in any electronic design nothing is absolutely perfect and there will be a bit of noise and a bit of "colouration" even on the best pre-amp. However, in any half way decent design, the effect of the pre-amp should be small compared to the "sound" of the mic itself. The big differences in sound come from the transducers, the bits that convert between actual sound and electrical signals. This is why when choosing a hifi it's the speakers that make the biggest difference. Yeah, the amplifier is part of it too but you'll hear a much larger change when you swap speakers than amps. It's the same in reverse with microphones and pre-amps.
There can be specific reasons for using an external pre-amp. For example, when I was working, we had a sound post production suite with professional acoustic treatment and some quite sexy equipment (Amek mixer, DAR soundstation system, etc.). For a major project we purchased a new Neumann microphone (can't remember which model) for the voice booth and, although it sounded great, the output was quite low. Rather than use the Amek pre amps almost flat out, we also bought a specialist mic pre that offered more "clean gain".
In other circumstances, using high end equipment, some engineers and producers will use a specific microphone and pre amp combination just for the colouration it will provide to the sound. The differences are relatively subtle--but when you're paying hundreds of dollars an hour for a studio, you're paying for subtle!
So, basically what I'm saying is that a great mic pre-amp won't fix a poor to average microphone--and, for your budget you won't get a great pre-amp anyway. There may be specific reasons to use an external pre. I recall a previous thread about a particular model of Tascam portastudio where the mic inputs turned out to be high impedance and unbalanced so they didn't work properly with standard mics. In that case, the kludge of a solution turned out to be buying a basic mic pre amp so the line inputs could be used. However, this was more by way of a "work around" than a desirable solution. I should stress that I don't know if this applies to your Portastudio model.
I guess the main thing all this waffle is trying to say is that, although external mic pre-amps have their purposes, they're not a magic bullet solution to all problems.
Bob