According to classical Theravāda would a Buddha or highly skilled Arahant be able to skip to say the 2nd or 4th Jhana without going through the preceding stages or do they always have to follow in sequence?
They still have to go through each jhana in sequence, although for those great ones in the past who had mastery this could all happen in split seconds ( as far as I know) 
3 Likes
The Visuddhimagga does mention skipping jhanas as one of the 14 ways of training the mind for supernormal powers. For example, one would enter the the first jhana in the Earth kasina and enter the 3rd jhana in the same kasina without entering the 2nd jhana, but to do this they would need to have mastered the 1st, 2nd, and 3rd jhana.
I would imagine a very skilled meditator can directly go from even the 1st to fourth jhana by letting go of the other jhana factors.
2 Likes
you are right. 
Visuddhimagga:
XII 2. If a meditator wants to begin performing the transformation by supernormal power described as, “Having been one, he becomes many,” etc., he must achieve the eight attainments in each of the eight kasinas ending with the white kasina. He must also have complete control of his mind in the following fourteen ways: [374] (i) in the order of the kasina, (ii) in the reverse order of the kasióa, (iii) in the
order and reverse order of the kasina, (iv) in the order of the jhána, (v) in the reverse order of the jhána (vi) in the order and reverse order of the jhána, (vii) skipping jhána, (viii) skipping kasina, (ix) skipping jhána and kasina, (x) transposition of factors, (xi) transposition of object, (xii) transposition of factors and object, (xiii) definition of factors, and (xiv) definition of object.
[…]
- (vii) He skips alternate jhánas without skipping the kasinas in the following way: having first attained the first jhána in the earth kasina, he attains the third jhána in that same kasina, and after that, having removed [the kasina (X.6), he attains] the base consisting of boundless space, after that the base consisting of nothingness. This is called skipping jhánas
2 Likes
Thanks both, much appreciated.