Exceed recommended power supply range on analog switch
The obvious answer is no. That's what data sheets are for.

However, it's tantalising to have an absolute max above what you want to run it at, isn't it.

The fact that the analogue inputs give a voltage specification with respect to rail confirms that the protection diodes are to the rails.

A serious problem is hinted at by the fact the digital absolute max is not with respect to the rails, but to an absolute voltage of 5.5 V. This is still above 5 V, isn't it? But it's a lot closer than the 7 V for the rails, and suggests there are lower breakdown devices inside. The same applies to TTL, and there the recommendation is not to tie inputs to VCC.

If you're a professional, or intending to sell this stuff, then the answer still has to be an unequivocal no. If you're an amateur, making one, and its failure is not going to inconvenience you beyond making another, then why not try it? You'll probably get away with it. Its failure mode is unlikely to be bursting into flames. 

If you're building it for a friend, then you're putting your reputation on the line, is that a thing worth risking? Don't post it either as a 'good' circuit, it isn't.

The manufacturer is rating this switch with their reputation in mind. They don't want to be known for 'fragile' products, so they will have built in some margin, which includes users sometimes having a bit of over-voltage on their rails. How much of that margin do you want to knowingly use up? You might want to put more effort into making sure the power supply doesn't spike. It would definitely be worth trimming a bit off the digital control voltage, or restricting its input current, as is the recommendation with TTL.

There are other analogue switches rated for the voltages you want, though this one has a rather nice low on channel resistance. Is that the reason for it? If so, consider designing with FETs, and you'll get even better on channel resistance, though at the expense of space and component count. Unfortunately, really low Ron often goes with low voltage, and a lot of designs today are targetted at single cell LiPo products, like phones.