"Would having a fence hinder the pool company from installing the pool?" If it is too close or if it closes off construction access. The solution to NOT having this happen is planning now, before the fence is installed. You could determine the location, size and shape of the pool, its decking & landscaping, and the location of the fence. By "planning now," I mean committing all of the ideas for the backyard to a piece of "paper" (electronic or not) ... on a PLAN (map) of your backyard drawn to scale.

Also check with your municipality for any bylaws related to pool or pool fence construction. For example, some jurisdictions have very specific requirements for fencing around a pool (height, design specifics that minimize climbability, self closing and latching gates, etc.). You don't want to build a fence now and find out later it won't get approved as a pool fence.

You might want to also check with your insurance company. We don’t have a pool, but it wouldn’t surprise me if aspects of your pool fencing and security impact your insurance rate.

Check with your poolbuilder or designer, but generally the equipment they use these days is ~6 ft wide. If you have the ability to remove a panel for the duration of the pool install you should be fine.

To echo Yard, you can never plan too much or too early. When you work with a landscape designer, that's the sort of thing we all do.