I did it this year with someone doing the driving. I would say it would be much safer with the support of a driver. I didn't get much, if any, sleep between peaks and by the end was completely shattered, completely!
i would say that after Scafell Pike (did Nevis first, Snowdon last) I would probably have been more of a danger on the road than someone who was over the legal drink drive limit!
The group we organised it with allowed 5 hours for Nevis, 4 hours for Scafell Pike and 4 hours for Snowdon. That was up and down on all three peaks, the other 11 hours was set aside for driving and was done in a speed limited mini bus.
If you train properly and can come in well within these times then there is absolutely no need to be hating around above the speed limit. I would suggest someone doing the driving for you, even better two people, and that would also allow you a certain amount of verification that you had done the challenge. Always plenty of people on the hills who would happily take your pic at the top for you too.
Dont underestimate it, it is a challenge but it's fun.
I managed Nevis in 4hrs 5mins, Scafell in 2hrs 38mins and Snowdon in 2hrs 50mins so was well within my times but lost 11lbs in weight for my efforts. I walk on average around 60 miles a week and have been at the top of 40+ Munros this year so consider myself to have a reasonable level of fitness. Your gonna need to get a helluva lot of calories into you too so plan well for that!
I sound all all doom and gloom - it's a great achievement, a good buzz and most of all if it's for charity it's worthwhile cause!
Enjoy!