Does subpixel rendering technology such as ClearType have any effect on CRT displays?

Not as such. The results vary from screen to screen between "blurry mess" to "nice and clear".

Most computer monitor CRTs have a shadow mask which has a triangular arrangement of colors.

Here there is clearly no way that subpixel rendering can work the way it should. However, you still get the difference in brightness and CRTs being blurrier than LCDs may make the text appear similarly to conventionally-smoothed text (which uses just grayscale to smooth the edges).

Some computer screens have an aperture grille and I happened to use one of those for several years.

Here you can actually have a similar effect as on LCD screens for ClearType, especially when hitting the maximum resolution of the display (I tended to do so because my eyes work and I valued the space on screen :)). However, there is no guarantee that every pixel will lie exactly at the boundaries you would like it to lie. Also with older monitors the dimensions of the image tend to vary with overall brightness of the image. But at least for me subpixel rendering on such a screen was superior to grayscale antialiasing.

When I used a 17" CRT on it's maximum resolution (1280*1024), I enabled subpixel rendering and it actually looked better.