I am glad you asked a very important question. The easy, assumable answer is NO, they do not "allow" sex offenders, felons on work crews... with that said;
Anyone serving time in a State Facility is a "Convicted Felon", thus, felons are on the work crew. As to what their specific crime is, that will take some work. I would think the list of inmates working on our roads, in our neighborhoods, would be public record. Anyone can search the DOC website and get photos and arrest history for anyone convicted. That might take some work and I doubt that Department of Trans and Department of Corrections will give this up very easily. I will go so far to say I doubt they have even communicated with each other on this.
As for Sex Offenders, I would not be surprised if one was on a work crew. Please understand, there is a large difference in being classified as an Offender or as a Predator. I do not think our State agencies are so inept that they would allow a Predator to do outside work. An Offender, perhaps.
Your question is one that depending on how far you want to take it, can open some interesting dialogue.
I recall an incident a few years ago with a Walton County Jail Inmate, along with two of his co-inmates, all working on a road crew as "trustees". The SO allegedly conducted covert surveillance on this crew in order to bust one of the Jail Employees who was being accused of smuggling Tobacco in to the jail, I think the guys nick name was "Croc" or "Gator". Anyway, yes, they were smuggling tobacco and it was discovered that the three other inmates (not smuggling tobacco) had an elaborate escape planned for that very day. They had a vehicle waiting for them and they were going to run from the group and flee. This would have worked as all were in good shape compared to the officers "watching" them. The plan was foiled and the three removed from the Trustee Work Groups.
Anything can happen when criminals are out in the public. Your security is only as good as the moral compass of the incarcerated and the ability of the officer, usually only ONE, to control the group. I would look into this further and request any documentation as to how the daily operation of one of these crews operates. That too is public record. It is an operational procedure.
Hope this helps.
w