it will run with 1 gb no problem at all ,
but it will run far better with the full 2 gb it can take and it even helps with youtube watching
the eMac especially the 1.42 models are very much underrated , because lots of people think "its got a crt screen so its totally ancient and therefore must be damn slow no matter what you do ", but thats a myth the eMac 1.42's are from 2005 and they shipped until mid 2006 so are only 4 -5 years old
maxed out they can even perform as well as the early 1.6ghz and 1.8ghz iMac G5 (if these are left in original spec , certainly they can outperform the eMac if they got maxed out too ), but the eMac is less likely to overheat, its heatpipe is massive
and the fan is really effective to cool that processor and the crt down and it is overclockable to 1.92ghz and according users who have done that it still wont overheat
so get the 2x 1 gb pc2700 and let the eMac fly, you owe it to him