If I own Yes shares am I allowed to purchase No shares to play a spread?
Yeah, it makes more sense when you're looking at multiple, mutually exclusive events. Unfortunately, when there's more than two options (as there would be, otherwise it would just be a single YES/NO event), you'd need to invent the concept of turning one YES share into many NO shares (and vice versa), and that might be tricky for the devs to implement. What do you do when someone puts in a limit order to buy a YES, it generates a sell order on a spread of NO shares, and then one NO gets bought and the others don't? Probably best to keep things simple and inefficient until the market gets a bit more liquid.
What you describe is not arbitrage, it's hedging.
The YES and NO markets are not actually separate though, so this question only applies to markets with multiple mutually exclusive options.
How did Intrade handle such cases?
What do you mean by saying that the NO markets are less efficient? YES and NO orders write to the same order book, and so they always have the same spread, and represent the same information...
It seems more likely to me that the YES price inflation is due to the much lower dollar tie-up of buying YES shares in a multi-proposition market.