No, alcohol is a rather different type of CNS depressant.
I'm not sure of the exact mechanism of the chemistry involved, but a classic beer includes psychoactives besides alcohol. Hopps are mood altering plants - try eating a pellet or two sometime. If you can get past the bitterness, it is quite relaxing. There is an old wive's tale that a sachet of hopps under one's pillow helps cure insomnia. The hopps harvest was, in days of old, an interesting time.
Unfortunately, the kind of beer that comes in cans doesn't have enough hopps to have any effect at all.