Can I electrically isolate appliances by putting them on separate legs of a split phase supply?
If the outlets are on completely separate wire runs from the breaker panel OR sharing a neutral but on opposite legs (sharing on the same leg is illegal), then the wire resistance from the panel to the outlets will be isolated between them and the voltage drop will be minimized. (The current draw is low enough that there should be no noticeable drop at the panel).

So yes, even if they were on the same breaker, let alone phase, as long as the wire runs are separate, the server should not see a drop from the laser printer. Also good if a neutral is legally shared.

(The reason that the shared neutral is OK is that each circuit's return current will be 180 degrees out of phase. Therefore, the worst case current through the neutral will be one circuit's. In fact, when the laser turns on, the voltage may even rise slightly to the server as some of the server return current will actually flow through the laser, bypassing the neutral.)