You might be over-thinking the weight and strength issues. You are going to be setting servers and monitors on this, not pounding them with sledge hammers. One inch is thick enough to hold that without bowing, especially if you are adding extra supports.
Are you doing butcher block because of the perceived strength, or because you want to create a beautiful piece of furniture? If it is for the beauty, go for it. If it is just for the utilitarian strength of holding PC machines, don't bother.
If all you are concerned with is strength, just glue two pieces of plywood together. Any thickness from 1/2-inch to 3/4-inch will work; perhaps a nicer piece of 1/2-inch hardwood plywood on top of a 3/4-inch piece of anything. That's going to be massive and strong; you could stand on it and jump up and down on it all day long and not hurt it or make it sag.
If you want to do the butcher block to create an awesome looking piece of furniture that could last for decades of pounding a meat cleaver into and still remain water-tight, then by all means do it.
The strength in butcher block comes from glueing the strips together. Cut and plane your boards, glue them up, and clamp them to dry. Glueing and clamping is the key. Pin nailing is a convenient way of holding the pieces aligned while you assemble everything. If you have a pin/brad nailer and want to avoid everything shifting around in assembly, use it. Don't bother buying one just for this if you don't already have it (unless you've been looking for an excuse to buy one; they are fun). The pins/brads certainly don't add any strength; that's all in the glue.
Butcher block is traditionally tall, narrow strips of wood. I've seen the pocket screw approach to create large tables from wide flat boards, but I don't know if I'd call that butcher block. I certainly would still always glue the edges of the boards together.
Whichever way you do it, you will still end up needing to plane it after all the glue dries, if you are looking for a smooth flat table-top. Doesn't need to be a power planer; a hand plane works as well.
So, ask yourself about what your goal is. You can certainly make a strong, fine-looking piece of furniture with the butcher block approach, if that's what you want. If you just want the strength, look into plywood.