The short answer is that it will affect your bend angle. You will have to make adjustments to your depth control, depending on your allowable tolerances.
Material thickness variations will cause variations in the finished part based primarily relative to your bottom die width of opening. The wider the die opening, the less variation. This is true for air bending, which is the most common. Dies which are specially constructed to bottom out will tend to peen or set the corner, regardless of slight material thickness variations, but this takes an operator with a little more finesse to avoid putting excessive tonnage on the press and tooling that may not be necessary.
How precise of bends are proposing to make (+/- what fraction of a degree) ?
Now, there are press brakes available with bend angle sensing that will correct for anomolies. If your requirements are very tight, this is definitely worth the investment.
It is better to have enough ideas for some of them to be wrong, than to be always right by having no ideas at all.