Sure he can. The more interesting question would be about quantifying his chances.
FYI, Hamilton was the pre season favorite by a long way from Vettel. Hamilton started 3.8 and Vettel 7.3. That is almost twice as bad as Hamilton. Webber started 20.3 pre testing season which was the worst score of the top eight drivers at that time.
Here you see how he was rated by the bookies/betters over the whole season. He came from nowhere and was pretty much ignored for a long time. His rating improved from P8 to P6 during testing which was more an issue of the car than personal performance.
After his recent good form he made progress in the odds but was still rated on P4/5 together with Button compared to Vettel, Alonso and Hamilton after his win in Spain. The second win in Monaco put him up to P3 now, which is quick progress. If he keeps outscoring Vettel I'm sure he will continue to rise, but the punters do not easily get convinced by a surge of form it looks.
Personally I see him better than Button.
Interestingly in a hypothetical situation where all drivers would drive the same car Webber would still be rated on fifth place.