Will AVR stabilize the flow of current?
There are two things you need to protect yourself from:


Over-voltage (which it sounds like what your AVR is for - it just trims voltage down when it's over).
Under-voltage (which often uses a battery and an inverter - when the voltage goes too low, it switches to the battery).


You need to determine which are part of your problems and fix them.

Generally speaking, under-power doesn't cause damage (and, in the case of incandescent light bulbs, actually increases their life).

Over-power is what kills things (like your laptop's charger, a monitor, etc).

And this is where things get complicated.


If your house looks like a resistor, then voltage and current are linearly related and the AVR can quickly suppress any over-power issues.
If your house looks like an inductor (hint: most houses do because of all the motors running), then the voltage will lead the current, and the AVR will still be able to trim the voltage.
If your house looks like a capacitor (I think this is unlikely), then the AVR isn't particularly useful for protecting your laptop against a bad power grid.


Another note: most modern electronics use switching-mode-power-supplies, which are good at handling surges (a good rule of thumb: if its label says it can natively handle 110-240V at 50/60Hz, then it's most likely a SMPS). Legacy transformer-based power supplies are not.