No, scaling up a banana to match the mass of the sun would not cause it to collapse and turn into a star. The process of stellar formation and the factors that contribute to the formation of a star are much more complex than simply increasing an object's mass.
Stars are formed through the gravitational collapse of large amounts of gas and dust in space. This collapse creates a high enough pressure and temperature at the core of the collapsing material to trigger nuclear fusion, the process that powers stars. The fusion of hydrogen atoms into helium releases an enormous amount of energy, which counterbalances the force of gravity trying to collapse the star further.
A banana, on the other hand, is composed of organic matter and does not have the necessary conditions to undergo nuclear fusion or sustain the energy output required to become a star. Increasing its mass to the mass of the sun would simply result in an incredibly massive and dense banana, but it would not initiate any stellar processes.
The formation of stars involves many complex physical and astrophysical processes that occur on a scale far beyond the capabilities of everyday objects like bananas.