Not likely. The best place for life to form is on Earth-like planets, with liquid water.

It is just a quite doubtful hypothesis. Life (as we know it) can be created at the presence of water, a reach variety of chemical compounds, some activation energy (heat, light, electrical discharges, radioactivity?) and lot of time. Comets are mostly deep-frozen bodies (particularly if travel through galaxy) so how could life be created on them, or how could life "jump" on comet from life-abundant planet ?

Not in the comet itself, it is known that the organic material enclosed in the nucleus of the comet is very well protected, therefore when it hits a place, the collision energy will generate hydrothermal systems induced on the organic material of the cometary nucleus, these systems can be maintained for millions of years and incubate microscopic life. Inside the crater a soup of organic material is generated as if it were a cooking recipe.

Moreover, it is very likely that life on Earth began in a similar way. This science is called, Astrobiology.

The real interesting problem is how life starts, whether on earth or elsewhere, and for now this is still unknown.

But what is now clear is that life on earth in bacterial form can be exported by asteroid impacts. When an asteroid impacts earth a part of the earth crust is melted, and a part is ejected without much heating. Within ejected rocks bacteria resist incredibly high accelerations, and if the ejected rocks are big enough (several meters) bacteria are shielded from cosmic rays and can survive the cold temperature of space. We know also that meteoritic impacts on earth preserve the content of the inner meteorite, so some bacteria inside a rock would eventually survive the impact on other bodies.

So I would not be astonished if earth bacteria have already been exported to Mars or to other interesting solar system bodies like Europa or Enceladus.

This is reverse panspermia.