Hmmm... That doesnt sound right. "I collect them all" you'd say when referring to a definite object.
Like "you seem to have a lot of baseball cards!" "Yes, i collect them all!"
While "I collect everything" means exactly that - everything. You're a person who has the abnormal habit of not throwing anything away!
I think the German word sammeln is "larger" that the English word collect, and encompasses a lot of your ideas here. For example, one big difference in my experience living in Dresden is that people go out "pilze sammeln" (forage/pick/gather mushrooms).
I think perhaps the English "to collect" has a stronger emphasis on the passive action "to store things which together make a collection" among its shades of meaning, while the German "sammeln" tends more toward the active gathering action, for which I sometimes use the English "to gather".