Can I use post being sunk for a sail shade as corner support for a deck?
No.  Deck beams must have bearing (direct support underneath).  They can not be supported via side connections.

It looks like from the image that you are trying to support deck beams on the 6x6 post without bearing at the post.  If these are meant to be beams then they must have something under them at the bearing point.  A side through bolted connector for a beam to post connection is not approved for decks.  I assume that the reason is the through bolt connection or wood could degrade under weather and is much safer if it is actually resting directly on a post (still requires connections).

The following guide lays out how to design/size beams for your deck in a prescribed manner.  The joists that span between beams can be connected via hangers and don't require direct bearing (something underneath).  If you vary away from the prescriptions in the guide then you'd need an engineer to approve of your variations.

See figure 9, prohibited post to beam connection.

https://awc.org/pdf/codes-standards/publications/dca/AWC-DCA62015-DeckGuide-1804.pdf

Probably the best thing to do is to upsize to 8x8 undressed (not nominal), then notch the post for direct bearing of a single beam.  I am assuming just a 2 member beam so you'd have to integrate that into the spans of your deck.  The joists that span between this beam and your ledger do not require direct bearing (see figure 8A).  Then to prevent a weak area in the 8x8 I'd get a 2 pieces of 1/4" thick steel 3x the height of your beam so if you have a 2x12 beam then 11.5x3 = 34.5".  I'd take the steel and laminate it on the beam notch side and the non notch side and bolt it together that way any forces from the sail or your railing assuming you are integrating a railing are transferred past the weak spot in the post.

Good luck.