In terms of drying times and rates hand finished concretes and screed dry at approximately the same rate in the same conditions. the actual rate depends heavily upon the ambient conditions. In general terms the accepted average conditions in the uk are based on 20oC and 60% relative humidity. This time of year however it is difficult to acheive those conditions and the drying rate is necessarily extended. It is almost impossible to give a firm answer as to how long that is likely to be. Many builders will use a sand cement screed or concrete and the standard time before covering is 6 weeks. More often than not people get away with this but the screed is unlikely to be dry enough after 6 weeks (unless designed to do so) to meet the active standards in terms of moisture content.
If, as Dave says, you use a decoupling membrane, which if you examine Ditras advice, it can be laid almost as soon as the concrete is hard enough to walk on. It acts as a vapour stabilisation layer and again as Dave has already said allows the moisture to move around within the cone structure of the mat and eventually to dry out. I am not sure what typoe of adhesive you would use as most of these of course say the screed should be at or below 75% RH (dry) but the Bal stuff may be an option.
The alternative is to impede the migration of the moisture by using a surface DPM. These can also be used very soon after the screed is laid (normally at 99% RH which will be after a couple of weeks tops) These do not appear to be commonly used by tilers but are used almost routinely in contract flooring particularly vinyls and the like. In these types of projects floors are rarely given time or curcumstances to dry properly and you cannot easily lay a vynil on a decoupling membrane. (they are available for vynils but rarely used) so a DPM is used. The damp proof membrane is generally installed using a notched trowel and works by sealing the moisture into the concrete and releasing it very slowly the same as the decoupling membrane. Some DPMs need to be applied in 2 coats and the second coat should be tacky when you lay the final covering. I do not like these as they can be quite messy so I prefer a single coat. If you need to imporve key you can sprinkle sharp sand into the DPM surface whilst still wet to provide a nice rough surface although in my experience this is rarely done and does not generally cause issues.
The moisture does no harm sealed into the concrete as it is made using cement and as long as there is water present this cement will simply continue to react and the concrete will get harder. Both systems will help to, cure the concrete and minimise the risks of curling.
The only drawback of the DPM would be if there is no allowance for horizontal movement within the concrete and it is required. This requirement is determined by the size of the bays. Horizontal movement is accomodated by placing joints in the concrete at suitable intervals. If it does need joints and they arent there the concrete could crack over time due to shrinkage. The decoupling mat can help to absorb this movement although do not rely on it to do this as it is not what it is designed specifically to do.
Neither systems are designed to replace joints either in the screed/concrete or in the tile face.
Hope this helps
Alan