It depends on exactly what you mean by "rich," but yes, many archers did indeed see significant benefits from their military service. The demographic of people capable of equipping themselves as mounted archers not only gained in wealth through their campaigns, but also were afforded more respect and prestige socially. Some archers and poorer men-at-arms did indeed become wealthy through warfare (whether in England's service or abroad as mercenaries), but other would have seen gains in wealth without becoming rich. Unfortunately, we lack the raw data that would allow us to calculate the wealth gained overall by archers, but we do see that many of them appear to have earned enough through loot, pay, or ransom that they were able to afford plate harnesses and subsequently became men-at-arms rather than archers. That is no small expense, and indicates that they were at least somewhat of means. However, not all soldiers were so lucky. Medieval governments did not have the sort of bureaucratic, legal, and economic structures of modern states that would allow them to continuously fund the monstrous expense of conducting war. Monarchs might have to put up their own valuables as collateral for loans to pay for raising armies and troops often went without pay for long periods of time. So while some soldiers might have gained in wealth, others could easily have ended up permanently disabled (or dead) through injury or disease with little financial gain.