Yes, and a quick search for viral in-vitro assembly will turn up tons of results. — it's a little more complicated than that! — but it's not usually done as such, which I will explain. Basically, there are four things you might want to do:
- You want to make large amounts of virus and study it. If so, then all you need to do is infect your cell culture with your virus and let it replicate. Some are obviously easier than others — from my own experience, HIV is pretty easy but Hepatitis C is a real PITA — but that's essentially it. This obviously presumes you already have some virus stock on hand for infection. You could also transfect the culture with full-length viral plasmids, which leads me to...
- You want to study some specific aspect of the virus. That's cool! Most people aren't just concocting virus. Generally, for viruses that humans can get, it's generally recommended/heavily encouraged to only use what you need for safety reasons. So, for example, you might transfect the one protein you think is important to see what it does by itself. After that, you might transfect the cell culture with the full virus, but with one important gene knocked-out. I used to make single-round HIV by using a plasmid for full-length HIV without a functioning envelope gene and another plasmid for VSV envelope; new HIV particles would be made infectious because of the VSV gene but after infecting they no longer had that gene anymore. Basically, a limited version of the virus, which leads me to...
- You want to make virus-like particles. These are one of the better-named things in science and are just what they sound like — particles that look a lot like virus, but aren't. Generally, they're empty shells. We can use these for all sorts of things, from vaccine studies to other genes and diseases. Techniques can vary, but generally it's similar to the above.
- You want to introduce some other gene to a cell culture system, using a virus backbone for transduction; think "I want to fix these cells... permanently." Generally, these viruses are usually based on adenovirus or lentivirus (aka HIV) because they will insert their genes into the cell's genome, so the gene will persist.
Item 4 is probably closest to what you specifically meant. Here's a free review on the use and safety of retroviral vectors in humans, and here's a nifty one in fish. As for which viruses it's applicable to, well, that varies a lot by virus, host, culture system, and so on.
