Hi again,
Well, it could work if the conditions inside the scope are such that the noise is either relative or the noise is injected into a stage before the variable gain of the scope vertical amplifier. You could probably get away with a 100MHz bandwidth but that's going to be a little bit of a challenge. If the noise is being injected after the variable gain however this wont help, so a simple test is in order to find out for sure. It could also be quantization noise which may or may not mean an improvement so you really need to do at least one simple test.
To test this, build up a simple op amp amplifier and see how the lower frequency rate signals look, like a 50Hz or even 1kHz square wave. The amplifier could have a gain of 10 which would be good for testing this principle on your scope. If it works right, you could look for a better op amp.
The circuit is quite simple really, an input resistor of 10k going from inverting terminal to ground, and a 90k resistor from output to inverting terminal, and plus and minus 9v batteries for the testing power supply. You then input your signal into the non inverting terminal and ground, making sure not to exceed an input voltage of about 8 volts. You could probably try this with the op amp you are using for your amplifier in this thread. If it works, look for a better op amp and maybe make some other improvements.
In theory if the noise affects the signal before the variable gain of the scope the noise reduction will be proportional to the gain of the external op amp provided of course the op amp isnt noisy. So for a gain of 10 the noise would be reduced 10 times, but even for a gain of 2 it would be reduced by 50 percent.
If you have a variable amplitude square wave, you could set it on 1v peak and see how much noise you get, then set it to 10v peak and see if the noise on the scope looks smaller relative to the signal itself. If the noise goes down, the op amp amplifier technique will help, but if the noise doesnt decrease, then the op amp might not help.