I note from the question you're not asking "how" it would be achieved but I think you probably need some gene editing / therapy for someone to be able to hibernate, the biological processes involved need to be identified first (because I don't think they have been yet?), the genes responsible for those identified & where to insert them in the human genome without causing undesired effects.
That aside lets look at what you did ask.
- Can you slow an individual's metabolism to the point where they wouldn't need to eat for 2 years?
Based on the limits you place on the question (that it's some sort of hibernation & cryogenics is off the table) the answer has to be no.
The longest period of hibernation I can find any mention of is 344 days for a bat in captivity so it would seem two years may be pushing it.
While you hibernate biological processes are slowed rather than stopped & the animal survives off it's body fat, your crew are going to starve to death while they sleep if you keep them in hibernation for two years.
I think it's unlikely you can beat the bat & slow a persons metabolism sufficiently for them to need no food for two years while they hibernate.
Clarification / Rationale: if you want to reduce body temperature during hibernation so far that cellular activity is negligible enough they'll need (practically) no food (metabolized body fat) or oxygen then you'll be on the very cusp of freezing them.
The smallest temperature fluctuation might freeze them, then ice crystals form & they're dead.
It's far too delicate a balance & the best way to mitigate against an accident is to just saturate their tissues with a bio-antifreeze. Once you've done that (if you can) there's no point not going the whole hog & just freezing them for the whole trip.
But then you've got cryogenic freezing, which is not hibernation.
Best case scenario, you have to wake them after a year & feed them a high calorie diet for a few weeks to fatten them up again then you can put them back in hibernation. They need less food & oxygen on the journey with a slower metabolism but these needs won't be completely negated.
Or you can (as Ynneadwraith suggests) drip feed them intravenously while they sleep so you don't need to wake them, which means they're being fed so the answers still no of course.
- Would doing so circumvent the normal aging process?
No it wouldn't, hibernation only slows the metabolic processes.
Small rodents that hibernate are known to have longer lifespans in general than similar species that don't so it's reasonable to extrapolate that aging is slowed a little, which is expected anyway due to the lower body temperature during hibernation & the slower cellular activity that produces.
If you want to stop aging you are going to have to freeze them.