Will an antenna's built in pre-amp make a difference to overall sensitivity?

Here’s a post from a user explaining amp vs preamp without all the user friendly-ness comparisons, they kind of cut to the point.

can’t find what’s meant - “densens”?
As for tablo’s amplifier, here’s a reference to verify:

The main difference between the Tablo and a traditional TV is that the Tablo has multiple tuners - so that you can watch and record multiple shows at once.

The drawback here is a small loss in DB when the signal is split. We use amplified splitting technology to mitigate for this loss, so it’s nearly negligible. In some rare cases, you could have one channel on your TV that doesn’t appear on the Tablo.

My personal take, fancy “HD” antenna’s marketed with an amp/preamp is largely a marketing ploy. (much like naming an antenna specifically HD compatible). To start with, you only get the signal you got - period. Amplifying or booting a bad or weak signal doesn’t make it a good signal. That’s not to say there’s not a place for these.

To note, some users will paranoiaily tell you splitting your cable will cause your signal loss, yes. But if you have a good signal to start with, splitting it and cable runs won’t kill it! My antenna is 25’ up. I have an amp splitter (distribution amp). Then a 10’ run to 2 TVs and a tablo ( split - split, split) TVs work flawless, very rare occasional weak signal lost recording on tablo.
The second split from the amp runs 50’ to the end of the house and split TV and another tablo. No issues with either, rare occasional weak signal lost recording on tablo.

There are users who’ve discovered “over amping” their antenna caused signal issues as well. So you can have too much of a signal. I’ve seen this on a signal channel, it’s not easy to trouble shoot.