The answer is “No.” And many people wonder why. I have met many men who would gladly serve as deacons, but they cannot promise to remain unmarried if their wife should die. Most cogently say, “How could I deny my children a women who would love them as their mother did if she died? They would need a new Mom.”
It is little known, but a married deacon whose wife dies can petition Rome for permission to remarry. See Deacon Greg Kandra’s cogent comments on this issue.
On some different lines, a married protestant minister can now be ordained a deacon and then a priest. His wife and children attend his ordinations. There are dozens of such married priests serving in the Roman Catholic church in the USA today who converted from the Anglican Church. Yet, a Catholic who has served as a married deacon for decades can not presently offer himself to serve the Catholic community as a priest. Many people find this state of affairs confusing, contradictory and confounding.
In 1965 there were 58,362 priests in the USA. In 2010 there are 39,993. There are 16,649 deacons where as in 1965 there were none (the Diaconate wasn’t yet restored). There are 17,958 parishes (more than there are McDonald’s) in the USA and 3,400 lack a resident pastor.
Most priests are in their 60s and 70s. Many theologians and even Bishops believe that many of our “permanent” deacons could easily be ordained and serve as priests, thus responding to the looming Eucharist shortage we have now and the lack of Eucharist in many areas we will face as half the priests presently serving will retire in the next decade or so. Presently, however, that option does not exist.