I guess you do.
For testing(and development) purposes I advice you setting up a development environment locally.
1. Setup a new epi site with episerver deployment center
2. copy(replace) episerver config and dlls into project - not web.config.
3. export data from live site into your new epi site.
i think that will cut it
The short answer is no.
Most of the functionality you could setup to work without installing epi4 it but some, like scheduler service etc, needs to be installed. For old solutions it might be worth considering setting up a virtual machine with the correct environments. This will make it faster in the long run to shift in a new developer when needed. That's what I'd do with an old epi 4 site (except advicing them to build a new one in EPi 7...)
I want to do maintenance, e.g. patches, in Visual Studio, for an existing EPiServer 4.61 site.
So the site and its database exist already.
Is it possible to develop and run the site locally without installing the EPiServer CMS 4.61 product itself?
(I already have EPiServer 7 installed on the development machine, so it would be nice if I did not have to install 4.61 too)