Well...That is a tricksy question Brian.
Firstly training a horse to drive (anything) is a fairly lengthy process which starts off with weeks of long reining, followed by weeks of long reining with a tyre and chain to get the horse/pony/mule used to the noise of/and pulling something. Then after they are doing well with that you need to get them in a training carriage (usually small and lightweight, one axle etc) for a couple of weeks (with a driver and a backstep on a safety rein and not actually on the backstep - not normally one on a training carriage anyway). Then you can start them in a proper carriage (multiple axle, articulated, whatever vehicle you plan on using with them) with a driver and again the backstep walking by their head with a safety rein and slowly over the weeks moving back until they are able to stand on the backstep and then it takes a few weeks before they are comfortable with that and stop spooking at things, they learn how to corner properly, to respond well to people getting on and off (things being put on and off) and other mundane things like that.
If you want a pair or team then you can skip the training carriage part and put your animal in with an older experienced one in a pair carriage, and then put it in a team (3 or more, usually 4).
Also you usually break the horse/pony/mule to drive when they are young, as the older they are the less likely they are to take to it. In addition to this you have to make sure that the person driving knows what they are doing (much harder than it looks!).
As a quick example, over the last 6 months my driving friend and I have broken in two rising 6 year olds to drive and we have only just got them going as a pair (been out with them about 5 times) and have just started them on water elements (ie going through puddles and small streams). We haven't been able to get them out everyday recently, but they were long reined pretty much everyday and in carriage every day/every other day for a few weeks. You can shorten the time like I said before by putting them to with a more experienced animal.
You do get Ride N Drive horses/ponies - they tend to have been youngsters when trained (our ponies are lead rein, show and drive ponies). Theoretically any horse/pony/mule should be able to pull something but it is all about the training - if you have an older horse (8/9 and above) then they are more likely to disagree with it and be dangerous. It can be very scary for them because it looks frightening, makes scary noises, is heavy (especially weird for them going downhill), the poles can feel restrictive etc, and the person is making noises behind you for you to move forward - it is all done off of the voice, whereas riding has leg aids etc driving just has the voice.
Well that turned into a hug post and my apologies for that. I would say that if you had time to put in the training then yes they could. If the baggage animal was trained to drive when it was little then it should be fine. Same with the riding animal, but like with all things the skill would have to be kept up. I would say that you could probably train an animal in a couple of months to drive if you were doing it full time for someone and someone just wanted it broken to drive and then they would bring it on, but if you were doing it for yourself it would take you closer to 4 - 6 months to a year depending on what you were wanting to do (eg we are going to be eventing with the ponies we broke in over the summer in single, pair and tandem - which is why it is taking us longer). If just a single then probably 3 months and you would have a working young animal.
If you want more info on any of it or a specific bit do say and I'll try to help.