Yes that works.
You need to do a few things to optimize the pick though, since Soraka jg (like many other ap squishies) have a hard time clearing camps.
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RUNES: Use 3x SPELLVAMP quints. Mix with some combination of AS/M.Pen Reds, Armor/ScalingHP yellows, and scalingMR/scalingAPorCDR blues
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Go 18-0-12 on your masteries page, running DFT keystone. Make sure to max the mastery for Spellvamp/Lifesteal on the Damage line, as well as the increased shield/regen mastery on the defensive line.
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Max Q first, then E second. Although those skills dont work on jungle/minions (Q damages them but does not give you heal, E doesn't do anything to them), it'll give you a very strong gank presence. Walk into lane, use your E first to silence(and snare if possible); follow up with Q and weave in AA's for damage. I suggest getting the blue smite item, and going for cinderhulk (for better jg clearing), OR runic echos version for more damage. Runic echos is probably the best jungle item for Soraka just for the pure stats and strength, tbh.
And remember, you're literally one of the squishiest champs in the game, with very little (but deceptively strong) damage/defense. You ARE going to get invaded by a better jungler; your best offense is defense, and retreat while trying to land Q>E combos on the enemy jungler as possible. Give up buffs or camps if you have to. The great thing about Soraka is she doesn't need a lot of expensive items to be useful.
The reason you use spellvamp quints is just like running Karthus Jungle; with 3x spellvamp quints plus the 8% extra spellvamp (I think?) from masteries, and the jungle item (not the dagger, the other one); you have a lot more sustain in jungle than if you ran AP or something else for quints.