you can try dropping that comp into a 1920x1080 comp and then scale it up to fit (the easy way is to select the nested comp and choose layer>transform>fit to comp). then click the option for continuously rasterize (it's the layer switch that looks like a little sun icon) and see how that looks.
any vector layer should look perfect, raster layers and effects will look soft, but you'll have to determine if it's good enough, or if you'll need to redo the comp at 1080.
To go from 640x360 to 1920x1080 is a huge jump in size. If your source files are large enough, you could nest it all in a HD comp, enable the "collapse transformations" switch, and then scale it up 300% and see what happens.... But I'm guessing you'll have to redo it at the larger size.