Theoretically, yes. It's very difficult to get all the components in the right order, temporally, spatially, etc. The production of whole gene sequences is already commonly done. Viral delivery of such genes has been experimentally performed for research known as gene therapy--the replacement of normal genes in cells lacking such.
A couple of years ago, attempts to build the polio virus de novo was in the news. I think it was briefly discussed on FR. The general response was that it couldn't be done because, of course, life cannot be created in the lab. Now it's been done, so viruses are definitely not life. For ethical reasons this is the position of Wimmer et al., the researchers who did this work. More importantly than ethical considerations is if it can be done, somebody will do it and it had better be us, so we know what it is about and know sooner how to combat potential ill uses.
No doubt it would be a huge undertaking. You are on or near the cutting edge of this, looks like. Would you think it is just a matter of time?