As alluded to above - the answer depends on the level at which you're looking at the problem.
At a pure hardware level, could a CRT, like those currently used in aircraft, be used to display synthetic vision imagery? Yes. The CRTs are in essence no different from conventional ones used with computers, and would generally be fine.
Now, going back a level of abstraction from the pure hardware level and looking at this from a systems point of view...no, you couldn't. The standard architecture for aircraft utilizing CRTs is typically that you have some systems which generate guidance or navigational information (i.e. the FMS), which generate digital information and transmit it via an ARINC protocol (such as ARINC 429) to a display/symbol generator. The display/symbol generator takes this information, which you can imagine to basically be a long list of variable names and values, and turns that into something a pilot would recognize. That output is then what is rendered on the screen. It's pretty rigidly constrained, and the symbol generator can only really produce precisely what's been specified in the list (i.e. artificial horizon, HSI, etc).
With some installations you pipe all those ARINC labels (variable names and values) straight to the display and it does it all onboard, for some others you have a standalone box which then connects to a display via something roughly like a VGA connection.
Modern aircraft with fully integrated synthetic vision systems tend to use a non-federated architecture, which resembles something closer to that of a central set of computers running a series of applications, rather than discrete black boxes. You'll generally have something closely approximating a graphics card, which renders the whole mix of HUD imagery, synthetic vision pictures and the rest of it, and transmit that as broadband video data (see ARINC 818).
If I had to take a stab in the dark....are you looking at the feasibility of upgrading the black boxes 'behind' the CRT displays in something like the older Airbus models, bizjets, etc? If so...the CRTs in those aircraft cannot be used simply as dumb displays, and would have to go, along with the symbol generator and the rest of the gubbins.