It is possible to convert colorspaces and keep the resolution the same. A good "RGB to TV" converter will do this. All these converters do is convert RGB to YUV and IQ modulate the UV part to create s-video or composite NTSC/PAL. The resolution and scan rates stay the same. The TV internally converts back to RGB and displays things just like a conventional RGB input arcade monitor (or whatever) would, but the colors may have some error, especially on modulated connections (s-video and composite). The conversion can in fact be done entirely analog (AD725 is a good example of a chip that does this). A digital conversion is also possible, and the results are equal if you're careful aside from miniscule (and totally imperceptible even to the best of eyes) round-off error.
Converting resolutions (ex: upconverting CGA to VGA) results in non-native display. However, some conversions are special: CGA to VGA and VGA to CGA (and others that don't occur in arcade contexts). In the case of CGA to VGA, each line can be displayed twice (line doubled). This results in scanlines that are closer together, but there can be no other scaling artifacts as this is a 2:1 integer scale in the vertical dimension. If the original CGA timed source is actually interlaced (480i) rather than progressive (240p), then more complicated deinterlaces can be done that recover almost all of the original 480p progressive frame, but the results are still not equal to starting with progressive video.
In the case of VGA to CGA, the video can be interlaced (display alternating lines of each frame). While this discards data, some people actually won't notice other than things being a bit more flickery (this is the trick used by NTSC and PAL television). This pretty much has to be done digitally, but the results are not the same as you would get from non-integer scaling.