I'm working on a site that requires WCAG 2.0 AA adherence, but although we try to make tab navigation usable on our sites, it does detract heavily from the design due to the strange borders and outlines being rendered when you click a focusable element.
My thinking is, hide all focus states until the tab key is actually pressed.
So, my question is, does this pose any potential problems with accessibility technologies for the web?
Remember that sometimes focus is placed on elements without using a keyboard, such as via script or third-party tools (like screen readers prior to page interaction). Also note that even screen reader users do not necessarily use the Tab key (for example, I can navigate the headings on a page by pressing H in most screen readers, and on mobile I can navigate a page elements without using a keyboard at all. Also note that some users with cognitive impairments benefit from focus styles even when using a mouse.
As such, if I were reviewing a site that disabled focus styles only until someone pressed the Tab key, I would still fail it for 2.4.7 Focus Visible. It might be helpful to read the Understanding SC 2.4.7 document for a little more context.
To answer your question, yes, removing it does post potential accessibility problems.
All that being said, I would instead challenge the designer to do what designers tend to do best — work within constraints. Come up with focus styles that are not distracting, with styles that are perceivable, operable, understandable, and robust (so, for example, it meets contrast minimums). It has been done before, so there is no reason it cannot be done again.