Yes, though there are some interesting possibilities here
First we begin with the Astral plane's traits:
Subjective directional gravity.
Timeless. Age, hunger, thirst, poison, and natural healing don’t function in the Astral Plane, though they resume functioning when the traveler leaves the Astral Plane.
- Enhanced magic. All spells and spell-like abilities used within the Astral Plane may be employed as if they were improved by the Quicken Spell feat. Already quickened spells and spell-like abilities are unaffected, as are spells from magic items. Spells so quickened are still prepared and cast at their unmodified level. As with the Quicken Spell feat, only one quickened spell can be cast per round.
As a bit of flavourtext, we get:
The Astral Plane is the space between the planes. When a character moves through an interplanar portal or projects her spirit to a different plane of existence, she travels through the Astral Plane. Even spells that allow instantaneous movement across a plane briefly touch the Astral Plane.
From a legalistic standpoint, there are no reason to hinder teleportation via the astral. It can be theorized that due to the timeless nature of the plane combined with the subjective gravity, a teleportation spell could function simply as a transit-system through timeless space-time. Therefore, activating that transit system while within the timeless space-time of the astral has no immediate impact on the spells: they are designed for rapid transit within the astral plane.
From a "this could be interesting to your game" standpoint, you could assert that teleportation spells cast within the astral simply produce violent (if mostly consequence-free) gravity shifts but do not remove the character from play during the transit.
Another potential tweak could be that teleportation within the astral sends to you a real demi-plane, causing the character to have to trek across the demi-plane to reach the terminus of the teleport. Temporal effects are entirely at the DM's discretion here, but there could be some absolutely fascinating consequences for conflict on the astral if this is so.