Wondering if this would be a good idea at all? No one around here really plays my style of music so I want to I want to play my songs by myself. I have EZ Drummer with tracks made and have bass and rhythm parts behind it. I was gonna play my rhythm and lead parts live along with the backing track.

It could be good cause like no one does it so it would be different, but could also be bad sound and not the same feel as full band.

Would it work?
There are loads of one-man metal bands, actually.

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Works, but you need skill and dedication, theres loads of YT guys that do it, and Wintersun is probably the most well known "real" band that records like that (well, the drums are real, but they are written by Jari anyways).
I think your main problem would be making sure you're interesting enough live - With a full band, there (should be) lots going on, but if the audience is just looking at one man play a guitar, standing still, looking at the floor, they'll get bored quickly. But, as is said, there are a few one-man acts. Not that I can think of any - Most of them that become successful start hiring studio musicians to play the parts, to fill out the band. I think Nine Inch Nails does this
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You're going to have to be really skilled to pull it off.
Commanding four(+) instruments is not some easy task, because if you have any weird way of doing something on one, it'll affect the rest.

By this, I mean I found when I did stuff on my own, I found that any weakness in understanding another instrument hurt me a lot. I've played drums, piano and guitar... but I've not played bass ever. Thus, even though I can write a bass line... it's sort of bland because the bass always follows the guitar.

Also, you end up getting locked into your own style of playing. With 2+ people, you have various talents used throughout. If you're a guitarist and you always accent power chords with a snare hit or cymbal, you'll probably do this in all the songs... whereas a good drummer will know his time and place to do so. If you don't prevent this, the record sounds amateurish (unless you do it really well).
: )