Memory, by itself, is not going to cause the Apple IIe power supply a
problem. You should be able to install as many memory boards as the
computer supports.
Some third-party power-supply manufacturers say that a fully-loaded Apple
IIe (one with every interface slot filled) draws too much power and that
you should install a higher-capacity power supply. However, we have not
found that to be the case. Instances of supposed excessive power drain can
usually be attributed to a damaged logic board, power supply, or interface
card. A fully functional unit should not need a power supply upgrade.