Access to Work almost certainly would not cover commute costs.
Lots of people have to commute, AtW cover the costs that are extra for a disabled person, that an able bodied person would not have - so for example, due to my disability I can't drive, and I need a specialist vehicle for my wheelchair so I can't use public transport.
AtW did pay a PA to drive my vehicle. They did not however, pay for the fuel costs, or the vehicle. My PIP pays for that.
So in the above case, if the person needed a PA to come with them, they'd pay the PA's hours and if using a 'pay per person' transport method, the PA's travel cost (train ticket, bus fare)... but they would not pay for the Uber itself.
Of course if you don't get PIP you're highly unlikely to get AtW (you'd need to be doing permitted work but considered disabled under UC, and if you didn't get PIP the chances of you getting that are very slim).