In many cases, yes, the use will set up their own browser for the font size / zoom state / custom styles that work best for them. I'm sure you do this too - just because you come to sit at a PC that has the mouse on the left and the browser zoom set to 150% doesn't mean you will just use it as you find it - you'll change the setup to work better for you, just as you would adjust the chair you sit at to be more comfortable too. Every user has their own personal preferences for how they want things to be set up. This isn't just an accessibility issue, it's human nature.
Either users will keep these user-specified in-built browser settings as the default, or will have preferences set up to change to when they encounter a website that is difficult for them to use - such as switching to a high-contrast colour combination setup they have configured in the browser.
WebAim.org conducted a survey in 2013 with low-vision users to see what assistive technologies and techniques they use:
+----------------------------+-----------------------+
|Assistive Technology | % of respondants |
+----------------------------------------------------+
| | |
|Screen Reader | 39% |
| | |
|Screen magnifier software | 47% |
| | |
|Browser zoom controls | 47% |
| | |
|Browser text sizing | 38% |
| | |
|High contrast modes | 30% |
| | |
|Customized page colours or | 19% |
|custom style sheets | |
+----------------------------+-----------------------+
They may also use these browser settings in combination with actual bespoke hardware (such as screen readers, magnifiers or even large high-contrast screens).
However, just because users can and do control the settings of their own browser doesn't mean you can forget about accessibility altogether and assume that the user can take care of that themselves.
Assistive technologies rely on the site markup being built to known W3C standards, and that means deviating from standards - even if the browsers allow it - means you're impacting on the accessibilty of the site. This means allowing the user to be able to set their own custom styles (i.e. not forcing the site to render links in light-blue with no hover state without the ability to be overridden by custom styles just because it messes with the design if people are allowed to change it at will).
Another thing to consider is the target audience of the website. If you are aiming at people where you know a certain percentage of the users will have a disability of some sort then including accessibility options within the site is advisable, even if the user is just going to stick with their own browser settings anyway. For example the Paralympics or the RNIB websites include accessibility settings in the page header. This shows to the user that they have been fundamentally considered when the website was built, and doesn't presume that the user will be comfortable tweaking browser settings themselves.