I'm sure you can.  But please don't start with what is probably the most complicated amp that DIYers build.  Start with a well documented kit of a simple amp like a tweed Deluxe - http://www.tubedepot.com/tweeddeluxekit.html.  The Deluxe is a great sounding amp yet is simple enough to start learning the techniques you will need to build more complicated amps.

..Joe L

Yes, you can build without reading a schematic. But if you can't read a schematic and don't understand what ever part does, don't expect to be able to troubleshoot any problems that arise.

Fender was pretty unique in making and supplying printed layouts, the vast majority of companies never did, but the Fender examples are incredible resources to understanding the concept of amp layout.

Let's have a little history/business lesson.

The people who built amps at Fender, Marshall, etc. were skilled labor. They were trained in the process, procedure and best practices to build tube amp. All the knowledge of soldering technique, lead dress, heat sinks, part placement, etc. were drilled into them in training. It was very much an extension of assembly line production. They were given a layout to show what went where; but layouts are often incomplete (they leave out things like filament wiring) because they assume a basic level of training and "common knowledge." You can build a thousand amps from layouts and not have to learn a single thing about which. part does what.

None of these people needed to know a thing about tube amp design or repair...that was a different department. It certainly helps if they can compare a layout to a schematic and not inconsistencies. Some kit companies have had changing or inaccurate layouts, and having the schematic makes it easier to compare.

The schematic on the other had is the road to the circuit, it shows every component and how they relate and interact in a simple representation. When designing amps and mods, repairing amps, determining voltages, etc. it's much easier to work from a schematic. It can take me minutes or hours to trace through an amp chassis or a layout to figure out what I can see in a second on a schematic.

If you don't see the answer to your question between the lines...yes, a mechanic type can build an amp, and they do build the amps for most commercial operations. But you need to really spend a lot of time studying and learning all the things that Fender, Marshall, Dr. Z or whomever sits people down in classes and teaches them before they let them touch a chassis. I'm on record for saying most people who try and build a kit...shouldn't. Most don't take the time to learn to do it right. They end up with unreliable or noisy amps. The reason people recommend starting on smaller amps is do you develop the basics before you tackle something that may need to have every wire placed perfectly to avoid introducing noise. Thankfully for you, the internet is infinite in amp-building knowledge and chassis gut shots to study.