The simple answer is yes, it can. Let me correct the sentence first:
I have seen a man like him.
You don't want to use the definite article here, because you haven't defined a specific man that you are referring to.
It would be more correct to say that you can use ever, never or before with experiential usage, not that you should. These sentences have basically the same meaning as one another:
Have you been to Delaware?
Have you ever been to Delaware?
Have you been to Delaware before?
As do these:
Yes, I have been to Delaware.
Yes, I have been to Delaware before.
(We wouldn't say Yes, I have ever been to Delaware; in this case ever would be an archaic form of always.)
No, I haven't been to Delaware.
No, I have never been to Delaware.
No, I haven't been to Delaware before.
There is a very slight difference in emphasis, but you would be fine using any of these.