You'll just end up with a bass guitar with an alternative tuning.
If you go GCEA in the direction that is LOWER pitched than standard bass EADG, then it's just a bass guitar with an unnecessarily different tuning.
It'll just sound like a deeper, lower pitched bass guitar, and will have to be played like a bass guitar.
The instrument would share almost no similarities to standard tuning GCEA ukulele in sound and playability.
It's theoretically possible, but you would require custom strings and custom modifications to the instrument.
It won't sound very loud on an acoustic bass, unless you plug it into an amp.
Some 5, 6 and 7-string basses, with the right strings and setup would actually cover that range.
If you go GCEA tuning to HIGHER pitched than standard bass EADG tuning, then you basically just have a very low pitched baritone-ukulele-like instrument.
This tuning is possible on regular baritone ukuleles using speciality strings from companies such as Guadalupe, or using specific classical guitar strings (simply tuning EADG strings from a classical guitar set usually works to tune up to octave low GCEA on a baritone ukulele).
This is also a tuning used in a type of guitar known as a "Baritone guitar", except of course a Baritone guitar has 6 strings (added bass strings: A, D and then GCEA).
On a baritone ukulele, it sounds like this:
https://www.youtube.com/watch?v=HCyLRHl0wEY
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In conclusion, the tuning is possible. However, it's not widely used as it is quite an obscure tuning that doesn't really give significant enough advantages over existing standard tunings. There are unlimited different ways you can tune an instrument, and many musicians do use alternative tunings from time to time. However, popular tunings exist for a reason - they have simply been found to work better in more musical settings.