League of Legends (LoL) Question: can he be a support?

Everything can be played as a support If you're brave enough ;)

The answer to that question is always yes.

Sort of. Warwick is a great champion, and his kit might not be BEST suited for the support role, however, he does have a lot of CC and his ability to tank skillshots is excellent. Warwick suppport might function somewhat like a discount-bin amalgamation of the engage supports, body blocking skillshots, CCing carries, interrupting dangerous channeling abilities (think Jhin, Malzahar, Xerath, Vel'Koz etc), and roaming for assists and impact, all the while peeling for your own carries. Please note however, that you are most likely better off playing Braum, Leona, Nautilus or any other tanky engage support. All in all though, yes, he could be played support, with a heavy emphasis on roaming.

Could be but I wouldn't say he's very viable at all.

Your E is an AoE CC which can helps you tank and protect your ADC since it reduces damage . Your Q heals you after every trade with the enemy bot lane. Your W can be used to locate enemies and roam as well as chasing enemies. Your ult locks down enemies and can cooperate with your E to create a CC chain. AND you deal hybrid damage so it doesn't have to be worried about.
Take Aftershock, Font Of Life, Conditioning, Revitalize, Celerity and Nimbus Cloak/Water walking and you will be just fine.

resolve and inspiration trees should actually provide enough sustain to survive until your CC is unlocked. Plus it's warwick, you don't really need any damage items to actually deal a lot of damage.

Yes