The EU isn't really big on accepting states that are tapped out in market terms and bloated on welfare. They have enough of those already.
They are interested in taking on undeveloped markets like Ukraine and Turkey as a market for the cores (France, Germany) goods.
The only positive thing for them about Scotland joining is that it is a relatively small place, so won't have a huge effect either way on the EU. On Scotland the effect might be significant (both good and bad), but the EU isn't going to modify its policies for a micro state on the periphery.
There are another couple of weird things about an independent Scotland joining the EU, the first is giving up currency control as joining the EU it would be a requirement to join the EZ (I don't think the Nationalists had a clear idea on what was going to happen as regards currency at the last referendum). Controlling your own currency is a key feature of sovereignty, and if done well it can be advantageous (of course done badly it can be catastrophic). The second is that the EZ really needs to implement stricter fiscal controls such as budget balancing and whether Scotland would be able to achieve this and still achieve the level of welfare state it currently enjoys. At the moment the EU fiscal controls are not strongly implemented (putting the entire project at risk) but at some point another financial crisis will hit, and budget controls will become mandatory as the EU moves more towards a superstate.
To me Scottish independence to me now doesn't really seem like independence. It's more, we don't want to be part of the UK but part of the EU superstate instead. Of course framing it in those terms doesn't really stoke the "nationalist fervor" vote.
Edit : Maybe independent to choose which superstate we wish to be subservient to would be a better description.