Yes.
On the
Canon cameras - I can't imagine that
Pentax,
Nikon, etc do this any different - you can zoom as much as you like in either direction and the
aperture doesn't change
unless you have selected an
aperture that the
lens can't do at all focal lengths, in which case it selects the closest apeture it
can do.
So at f/11, it will never change at any focal length.
With, say, an f-3.5-5.6
lens, if you set f/8 it will never change.
If you set f/5.6 when zoomed in, the camera takes that as a hint that you want the
lens to be wide open, so as you zoom out, it will go to f/4 and eventually f/3.5.
If you set f/5.6 when
not zoomed in (i.e., at any focal length where you can have less than f/5.6) the camera takes that as a hint that you want f/5.6 and does not change it no matter what you zoom to.