Can adults compete in fencing?

Absolutely, and in more ways than most beginners realize. Open local tournaments welcome all ages, and USA Fencing runs a full Veteran circuit (40+, in ten-year age brackets) with regional events, national championships and even a world championships. The veteran community is famously welcoming to late starters because half of them ARE late starters.

A realistic arc: an adult who starts from zero and trains twice a week is typically ready for local open events within a year, and competitive in veteran events soon after, épée especially, where patience and point control age well.

Also completely normal: never competing at all. Plenty of adult fencers bout at club night for years, get the workout and the chess match, and skip tournaments entirely. Both versions count.