This reminds me of a certain company in the medical field that introduced a way for patients to fill out their intake forms on a touch screen tablet while in the waiting room. It sounded like a good idea but wasn't very successful. I don't know all the factors in it's failure, but I did hear of multiple practices saying that it actually slowed down their process. Perhaps because typing on the virtual keyboard is not as efficient than typing on an actual keyboard. Or perhaps writing a fair amount of words on actual paper is faster overall for most people.
In the projects I have been a part of that involve touch screens, we generally try to minimize the amount of typing required within the app. One way to accomplish this is to have predefined options, such as drop down lists/pickers or auto completing tags, or simple check boxes, etc. All to avoid the time it takes to actually type in data values, where applicable of course (not as applicable to names or phone numbers, but for most everything else). This can streamline data entry quite well, so if you are going full on digital, I strongly recommended exploring this direction. Be sure to cater to some of the more repetitive workflows of your users.
Although dealing with stacks of paper, then scanning large amounts of these physical forms, seems like it is not the best solution, it is definitely one accepted by most industries as how they enter in multiple forms and documents into a customer's/patient's file. I've never really liked this solution myself, but it gets the job done and keeps business flowing, so I would not rule this option out.
As a side note, if you equip employees with tablets worth a few hundred of dollars and send them into some of the rougher neighborhoods, there is a concern for their safety as well. If all the employees are carrying around is a bunch of papers in a folder, they are less of a target for theft than if they had an electronic device worth stealing. If this is a realistic fear that some of your employees may experience, then their user experience may suffer as a result of this, not to mention their overall happiness with their employment.
Ultimately, if your reasons for going "completely" digital are compelling enough, then I would try to streamline the digital data entry as much as possible, with the end goal of being faster than if filling out that same data on paper.