It is possible to collect everything, I have about six or seven hundred items left to collect before I have everything, but it is extremely time consuming as the closer you get to having everything the stingier the Sticker packs get with awarding you customization items.
I'm not certain how, or if, the various special Holiday related items could be obtained if you missed those the first time around. Theoretically I suppose Rux could wind up offering them since he's supposed to only offer that which you don't already have in your Sticker Book and there's always the possibility that the events will repeat again the next time the specific Holidays roll around again.
