I don't think that's likely - if you have ever seen a brake fluid reservoir, the fill level is almost always only a few mm below the actual cap level. It's pretty hard to overfill a hydraulic braking system due to that.
Checked the reservoir today - it is 2mm over the max marking - don't have enough experience to know if that makes any odds or not though wouldn't have thought so - the cap level is 1cm above that.