Yeah, silicon diodes refer to a type of rectifier which is a device which most often converts AC (alternating current) to DC (direct current) which is what the amplifier needs to operate. Tube rectifiers (usually a 5U4 tube in Mesa amps) have an inherent delay in their ability to convert AC ==> DC that is simply part of their nature. This is known as "sag". I would assume that the louder you go, the greater the sag is, as the amp is commanding more power to produce the increased loudness.
In terms of actual effects on your tone, a sagging rectifier tube will create a less precise tracking, meaning that very fast passages will be slightly muddled together, for lack of better word. It's not a bad sound at all, lots of people love it. I would consider 5U4s to be more organic when compared to a silicon diode. Silicon diodes are criticizing in their precision. In my MKIV, the tracking is so precise and accurate that I cannot outplay it, meaning that I cannot play fast enough to muddy the ability of the diode to convert AC to DC. This has benefits for metal players, because you can do those tell-tale speed riffs which have an enormous, percussive and brutal bass thud to them which you can certainly feel. It's a really empowering feeling. Playing with tube rectos is awesome too. It all comes down to taste.
But to answer your question, switching to silicon diodes ONLY affects the rectification process of your amp. The preamp (tone stack) and the power amp (amplification) are still all-tube driven.