No, the length of the year has no effect on the seasons other than their respective duration.
Seasons are caused by the axial tilt of the Earth, not by the length of the year. The length of the year only determines how long the seasons are in absolute terms, but their relative duration would still be the same. Spring would still be a quarter of the year, same as summer etc.
That being said, Earth's axial tilt does vary over time, on a ca. 40,000 year cycle, with the moon acting as a stabilizer. If you design a world with a much longer year and a much shorter axial tilt cycle, you could make your variable seasons per year work.