If we're talking about a true CRT monitor, then the input signal is basically driving the display directly. So there is no delay (other than the time required for the electrons to travel through the entire circuitry, which is negligible).
Late-era CRT televisions would have digital post-processing filters and such, which means the signal would get decoded and digitized first, then processed, then turned back into steering signals for the CRT. The latency depends on how fast this processing logic is.
I do not know of any CRT monitors that have such post-processing, but who knows...
In the case of LCD, you always have some digital processing logic. And if you feed it with a VGA signal, it will digitize this first, which may have additional delay compared to using DVI-D/HDMI/DisplayPort.
The actual latency will differ from one monitor to the next, and I believe I've seen latencys of over 30 ms on some models.
On TVs the processing is actually so long, that they have introduced special 'Game mode' settings which bypass the processing to reduce the latency.
So TL;DR: Yes, there's nothing faster than a CRT. LCDs suffer from latency, some more than others. This means they are not very suitable for a reaction test, unless you know what latency the LCD introduces, and this latency is within the margin of error of the total reaction time (which it probably isn't with 30+ ms).
Also, don't forget that there can also be delay on the computer-side, if you are using double-buffering or even triple-buffering.