can [it] be grammatically correct to only use "am" as opposed to "I am" or "I'm" if an "I" precedes

I'm sure we've all wondered about this.

It seems to me that writing is similar to the art of painting. Once you've mastered the basics, you can forget all the rules. In fact, to really excel, you must forget them, just as a painter forgets the mechanics of each brushstroke.

Personally, I think one should feel the rhythm of the sentence. In this case, the rhythm of the sentence is slightly amiss without the addition of "I'm".

Generally speaking, less is more in the composition of a sentence. This is one exception.