The short answer is no.
Earlier this year I redesigned a clients site and produced a lavish Bathroom site to replace an earlier style of site which looked around 5-10 years out of date. As is usual after a major site change sales dropped off briefly as returning customers did not recognise the site, but once over the initial lull things returned to normal. Sales didn't increase due to the site redesign.
This sales pattern has been pretty consistent every time i've overhauled old sites. The design of the site is completely irrellevent to whether you make a sale or not.
I have some motor racing related merchandise shops (i'd post links but we're letting the sites die off as we're dropping the lines).
2 are based on an older website design and 3 of them are very similar in style to the bathroom site and have more features like a fancy zoom and slightly better site navigation. The newer sites take more design cues from industry leading retailers but aside from the ocassional boost when particular drivers win Grand Prix the sales are comparable between the older and the newer sites.
The bottom line is that the design of the site matters very little. Top end web designers can charge quite a lot of money to produce a stunning visual design and i've seen CEO's and MD's of various companies haggle over minor aesthetic details for hours on end - and none of it matters.
What matters is the basics. Your site must imbue trust and your product information must be good. There should be no hurdles to purchasing, and you must be priced correctly.
Get these things right, adword efficiently, and you're onto a winner.