I haven't tried it, but on reading the enterprise deployment documentation for iOS devices, it sound feasible. My understanding is that you can for example, lock down an iOS device so that it can only connect via VPN to the Internet. The VPN end-point would be your own corporate servers, thus subjecting the iOS device, where ever it is, to the same filtered Internet the in-house employees get. It also means the iOS device effectively operates inside the company network, and is able to access the usual corporate intranet services.
Android is not something I've looked into. We had a couple of projects that wanted to use it, but they had great difficulty securing the systems to the satisfaction of the Information Assurance bods. That was a couple of years ago though, so maybe things have changed. I haven't seen the security model of Android either, as I have for iOS.
There was a report by the SANS Institute in late 2011, that describes how some of the techniques, like those native to the iOS Enterprise deployment tools, can be implemented, but at that time they were pretty much a DIY job. This involved getting messy with command line access to the device over SSH. That was a year ago, so I would be surprised if things haven't moved on and Google and third parties haven't developed tools and scripts to automate much of this.