There seems to be some confusion in terms here. An increase in the amount of available gil is an increase in the supply of money. At most this would represent growth in the economy in nominal terms, or in name only. Economies grow because productivity increases. In this case it would grow from the availability of more goods at lower prices on the market board, or an increase in the availability of services such as melding.
If the amount of gil entering the economy exceeds the amount being sunk then there will be some level of inflation. Low level inflation is ideal. Your concern about deflation is justifiable as any level of deflation causes an economy to grind to a halt. However, while dungeon rewards in terms of gil are limited, and repair costs are much higher, many players occupy a good deal of their time with fate grinding which offers better returns on gil per repair.
An experiment may be warranted, but in this case your results would likely be skewed by non-response bias.