Can a Planet Turn into a Star through Gas Accumulation?

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Would it be possible for a planet by collecting gas to become a star. I mean if it were to collect enough hydrogen, the temperature and the pressure at the surface of the planet could get high enough to start fusion ?
 
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The minimum mass required for spontaneous fusion is about 10^28 Kg [around 20x the mass of Jupiter]. Assuming the composition is amenable to fusion [lots of hydrogen], the core would ignite once the former planet accumulated the necessary mass.
 

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