I think "cheap" has various meanings. It all depends on what happens to be "cheap" about the guitar - electronics or build.
I've chronicled the mods to my Washburn HB-30 before, but I'll revisit them because the topic is germane to the thread. My Washburn HB-30 was all of $278.00 on ebay. MSRP is a few hundred dollars more than that, so maybe it doesn't really qualify as a cheap guitar, but it is thousands of dollars less than an ES-335. My HB-30 was made in Korea. Although it has the name "Washburn," like most guitars made in Korea, it was actually produced by the Samick Corporation.
Anyway, the guitar's overall fit, finish, and playability are actually pretty good. But, the electronics were quite sub-par, in my opinion. That guitar is one of my modding platforms and I've replaced every bit of the electronics, including the pickups. Until I finished my recently completed Les Paul Studio project, that Washburn was the only guitar I have for which I have received unsolicited compliments about the tonality and sound.
Beyond that, the control placement and ergonomics of the guitar are such that I actually prefer it to an actual ES-335. Sure, I'd take one if I found one inexpensive enough, but the control placement would irritate me after awhile. Some guys get hung up on neck profiles; I don't. I do, however, get hung up on control placement as far as suits my individual preferences. So, addressing the idea of why I don't just save up for an actual ES-335, I simply don't want one.
So, do I think you can take a cheap guitar and make it sound great? Yes, I do. But, it depends on the quality of the actual guitar. If the only really cheap things are the electronics, those can be replaced and you can have a fine sounding instrument. (Though, if the headstock doesn't have the "right" name some folks are sure to hear a difference!). But, if the actual build of the guitar is poor, results may vary quite a bit.