A great song recorded on crap gear, will still sound like a great song.... and still sound like it was recorded on crap gear !
However, 'budget' gear does not equal 'crap' gear. You can absolutely do stellar recordings and mixes in a budget home studio. Besides that, lots of commercial (and successful) recordings today don't involve 'large analog consoles' at all: stuff is being recorded straight into protools and the likes, and mixed with plugins only. This is the same technology and plugins that we have access to within the 'budget' realm of things. And with even all the DYI stuff available on the acoustics side of things (think basetraps and such), we do actually have 'budget' access to pretty high-end stuff these days.
Now, if anyone can get me a impulse-response of the famous Sound Citty live room (now Fairfax Studio)....