Fallout 4 – Can All Perks Be Unlocked?

Yes they do scale but this seems to only impact areas you've not visited before.

How did I test? Increased my level to 200 and stomped on all of the level 10 enemies for a bit, then moved to a new area I hadn't been to before, encountered a level 201 legendary and ran out of ammo before I could take him down.

The perks screen uses fading to indicate a skill you don't have, and outlining to indicate a skill you can't have (due to not meeting the requirements), see this screenshot here:

If you've got skills that are faded out, you should be able to get these by clicking on them and then pressing the confirmation key as prompted at the bottom of the screen:

If the perk is outlined entirely, hovering over the perk will still tell you what it does but also inform you of why it's outlined (not enough strength in my case).