Sure, but Astral Form isn't Astral Projection.
Astral Projection is all about leaving one's body inert and defenceless as its Essence leeches away while its mind has been peeled off and floats about elsewhere in a more vulnerable state because channelling mana without the physical body is more draining and causes Physical instead of Stun Drain. If the projection cannot find and return to its body in time before it runs out of Essence, it dies; it might be able to trace its silvery cord back to the body.
That's the gist of Astral Projection.
A spirit is
less vulnerable on the astral plane (SR3 core book even records spirits as being reluctant to Materialise because it makes them more vulnerable). It doesn't have an Essence count-down clock running. It doesn't have to pay higher drain by virtue of being disembodied.
So Astral Form is in many ways the opposite, not the same. I suspect it would be messy to try to copy verbatim the rules for people projecting and try to paste it over a spirit's repertoire and expect it to make sense or work sensibly.
Now, you could fabricate house-rule lore rationale that reveals conjurers on Earth summon spirits by creating astral shallows / alchera
on the metaplanes that force spirits to
astrally project from the metaplanes, leaving behind their natural "bodies" inert on the home metaplane, as its Essence leeches away over time, causing the spirit to depart at sunrise / sundown / after a year and a day / whatever because that's when the countdown runs out, and in the mean time one could trace any spirit's silver cord back to its home metaplane to its inert "body" if one wanted to go on a metaplanar quest to do so. By the same logic, (normal) astral gateway and alchera on Earth are likely the result of
metaplanar conjurers summoning
us to the metaplanes (where we "materialise" onto the metaplane) to perform some task, and as soon as our task is completed we depart from the metaplane exactly like how a spirit departs from the material at the conclusion of its services. That would be pretty cool lore and exploring that mirror world where we are the pawns just as often as the chessmaster would be fun (your metaplanar summoner is named Mr Johnson, the Dweller on the Threshold is his Fixer, and here are your tasks to carry out...), but I don't think we could consider it to be canon.
We have also discussed similar ideas recently:
so maybe any of the comments there could incidentally shed light on this.