I don't think anyone has really answered your initial question about whether or not Edward A. Cockey, II left the original deed to the land that Cockeysville now sits.
There were two groups of Cockey's in Baltimore Co.: Thomas & his descendants and his brother John & his descendants. They lived in three adjacent valley's: Limestone, Worthington and Greenspring. They also intermarried frequently and so it can get really confusing trying to figure out who belongs to which group.
Thomas Cockey had four children with Penelope Deye: Thomas Cockey Deye, Charcilla Cockey Deye, Charlotte Cockey Deye and Cassandra Cockey Deye.
Thomas Cockey Deye was the primary beneficiary of the substantial estate of Thomas Cockey. He was a Colonel in the MD militia, a representative in the State Assembly, Speaker of the House and was a member of the MD Constitutional Convention. He acquired lots more property after his father's death as well. His initial inheritance included Taylor's Hall, the family seat of Thomas Cockey & Penelope Deye, which if it still existed was in today's Cockeysville (which if I am correct is really part of Limestone Valley or perhaps Worthington Valley).
Charcilla Cockey Deye married her first cousin, Joshua Frederick Cockey, son of John (brother to Thomas) and Elizabeth Slade.
It is my understanding that the descendants of Charcilla C.D. & Joshua Cockey (and to some extent her sister Charlotte who married Thomas Ford & who's descendants married descendants of John), who are the "Cockey's of Cockeysville".
I have looked at all the data I have with me (most of my hard-copy stuff is in storage) and it appears to me that Edward A. Cockey & his descendants were the Cockey's of Greenspring Valley, descendants of John and not the Cockey's of Cockeysville - descendants of Thomas through his Cockey-Deye children.
So the short answer to your original query is probably No -- unless and here's where I don't have much information there is a connection to Cockeysville Cockey's via the Brown's. I am deficient in Brown data and don't know exactly how Susannah D. Brown, wife of Charles of the 1st Edward A. was his "cousin", but I know there was a Brown connection there somewhere. So unless the Brown connection is through the descendants of Charcilla & Joshua or Charlotte, it's unlikely that Edward A. inherited any of the Cockeysville property.
Perhaps someone else (Brad Lawrence?) has more data on this particular connection.