Speed helps with intercept, which gives you a good % (I think around 5-20%) of the attacker's denars. It's a good stat to boost for passive side of things and if the attacker has lofty unclaimed money that's a lucky day!
Correct me if I'm wrong, for starters we get up to 5 unclaimed denars, and it costs 10 to upgrade the vault. If you have high speed, then you might also want to up your unclaimed limits (vault level).
Yes, I think increasing your Vault level is required to make sure if you do benefit from an interception that you can hold the Denar till you claim.