I definitely know you can 'pass' event items on to the next event this way. I used to go through and accept all my presents EXCEPT my raw puddings so when shards would start, I could take raw puddings obtained in Elite Guard and get a quick boost of wins and shards. Since shards is such a short event, any 'free' pudding items makes a huge difference. Even with a couple slayers, it's definitely a challenge to get 2000+ shards to get all of the new cards. It's even somewhat hard to get 300+ streak because you have to get at least 50-60/day. That's not SUPER hard, but it requires some dedication and grinding.
In truth, raw puddings are almost useless for Elite Guard (I THINK EG is next... I can't keep up) but if they continue to use burgers/shakes, then temporary event items will be really useful again in EG. With the 24 hour clock, you can't afford to keep raw puddings in your inventory unless you're really sure you're going to need it. In some cases, by the time you drop back to the main page and accept the present, whatever SEG you wanted to hit has already been finished.