The way I understand it in theory yes.
Though tap pressure would deplete the resin very quickly! the slower the flow the longer it will last, better to have a tank of tap water then a pump to the di at point of use. And if your in a hard water area or a tds into triple figures without an ro then I would'nt even bother. Incidentally I'm in sussex where I think a hose pipe ban is still in place, if I was to connect a di straight to a mains tap I would be breaking the ban.
Thats the way I understand it anyhow.
Someone else on here may know better than me.
Simon