Hi Paco, you are much more of a teacher than I am but this question sounds very intriguing. So I did some looking around and, if you don't mind, here is what I came up with.
Since the song was composed in 1834, I am thinking the term 'plea' may have an older meaning that is not often used these days. The most plausible definition I came up with is:
From Miriam Webster:
3 : something offered by way of excuse or justification <left early with the plea of a headache>
Using the above definition of "excuse/justification" then you can say that "I come to you just as I am, with many imperfections. I am not making any excuses for my shortcomings. I am not trying to justify my wrongdoings. I admit I am a sinner. But by believing that you died for a sinner like me, I know I will be redeemed."
I think the theme of this hymn is repentance and forgiveness.