First of all, what amplifier?
It's not a given that raising ISO involves an amplifier. And no raising ISO does not cause noise. ISO is either noise neutral or in fact it suppresses noise.
That's one of the cases where I've often had to help one of my students who had unfortunately already been triangulated by the Internet. I'm in class looking at my students photos and the exchange would go something like this:
ME: These photos really are too dark overall.
STUDENT: Yeah, I was trying to get photos inside without a flash and I couldn't lower my shutter speed any more -- half of them are already blurry.
ME: You raised the ISO to 1600, raising the ISO was the right thing to do you just needed to raise it higher.
STUDENT: I didn't want the photos to be any more noisy. I figured I could go with ISO 1600 noise and then try and improve the photos in Photoshop.
ME: If you had raised the ISO higher, using the same exposure you'd have less noise.
STUDENT: What? The noise get's worse as the ISO goes up right?
ME: Wrong. Where'd you get that idea?
STUDENT: Youtube tutorials.
ME: The noise get's worse as the exposure goes down -- the noise is not caused by ISO. In the case of your camera a higher ISO with the same exposure would further suppress read noise and your photos would look better.
ME: Let's do some tests with your camera and I'll show you.
Here's a photo that I took for class as part of our discussion of ISO: APS-C sensor camera (Fuji X-T2) at ISO 25,600. No special noise filtering used -- no Topaz AI or DXO deep Prime -- just standard processing through C1:
ISO-25K.jpg That's the highest ISO on the camera; it's not causing noise.
ISO correlates with noise. Correlation is not cause.
If you're shooting camera JPEGs the ISO/noise correlation is pretty strong and you can't do much to modify it -- as you note changing ISO changes the exposure you have to set, but it's the exposure that causes the noise. However if you're shooting raw the ISO/noise correlation can be pretty weak (depends on the design of the specific camera) and it may be possible to do what I did in the photo I linked -- basically break the correlation because ISO doesn't cause noise.