Yes, the exchange rate for the dollar can impact the value of your savings. If the dollar becomes stronger compared to the Naira,, then the Naira value of your savings will increase in value. Conversely, if the dollar weakens, the Naira value of your savings will decrease.
In the long run, the dollar has typically gained value compared to most currencies, which is one of the reasons it is considered to be the safest currency to store wealth.