I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds B4 1840 are sparse.
For Thomas Gaughran B 1855 +/- 4 yrs in Co. Meath, I found 3 B rcds: 1852, 1854, & 1857. None were in the RC churches of Drogheda. One of these MAY be for your ancestor. Only 1 Meath RC parish was not rcd'ng Bs by these dates.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.