Q:

Would an alien species need to produce waste?

All organisms on Earth produce waste. Whether an organism's respiration has a byproduct, or it just doesn't process all food it consumes, it will always put some amount of matter into the environment after consumption.
Would this have to be true for an alien? i.e.
Could an alien organism choose and process food so efficiently that only excess energy left its body? Is this biologically possible?

A:

It's not about choice! 
Evolution "chooses" the minimal cost of living. Waste disposal is costly. So on Earth organisms that create less waste are preferred, "chosen" already. 
Why "no waste" is not plausible? 

Feeding and breathing. To get energy we turn substances with high chemical potential and turn them into substances with low potential. You need to discard used ones. Unless you can recharge using direct energy like light. Sadly, all ways to biologically turn light into energy are not really high power. Not enough watts from human skin area to power up one human. So you would need to handwave it, or came up with "fueling" unknown in nature. 
Feeding and growing. Only way to have no waste is to only allow precisely what you need in. You'll need to have food that matches composition of your aliens. Exactly. Possible? Maybe. Believable? No. 

