Probably what we'd see is an initial rough patch, then things would be basically fine for a while, then when the recession hit in 2007, Britain would be in much worse shape than it is now due to inability to devalue and problems with the ECB's deflationary bias.
The interesting question would what impacts Britain's participation in the Euro might have on the shape of EU institutions. If the U.K can tip the balance of power away from the German inflation hawks, then the E.U might be more disposed to economic growth in the '97-'07 period.
There's still going to be the problem of monetary lock-in which will cause the same problems we've seen in Greece, Spain, Portugal, Ireland, etc., and the E.U still lacks a fiscal union that's necessary for counter-acting the monetary lock-in.