Not very well. 9-speed cogs have closer spacing than 8-speed so the shifters won't move the derailleur enough. You will get adequate shifts for a couple in each direction if you line up the middle cog exactly but it will be ragged at the extremes. You certainly will need a 9-speed chain.
Cassettes and chains are the cheapest part of any upgrade so you might as well get them right from the beginning.