No, that won’t work, I’m afraid,
You’re right in saying that “ago” refers to a past event.
But the construction “may have been left behind” is used to indicate a possibility that something happened in the past, it is NOT a statement of fact.
He may have been here - there’s a possibility that he was there, but I don’t know for sure.
In my humble opinion
“Have been left” here isn’t a present perfect but
“may have been left” is a perfect conditional.
may ~ a modal
have ~ the first auxiliary
been ~ the second auxiliary used for passive voice
left ~ main verb
Modal + have as the first auxiliary + main verb ~ perfect conditional, active voice
Modal + have as the first auxiliary + past participle of the verb to be + main verb ~ perfect conditional, passive voice
This form can be made using another modals
I could have done this
I must have done this
etc
Different modal determines different meaning of the form (perfect conditional) and the complete sentence of course.
I’ve just said how I, as a learner, see the form.
I know grammarians would say that “may” is a verb here, it means the first auxiliary.