The answer to the question depends on how complicated one want’s to make the conversion.   

I’ve been running Spider God’s Bride (SGB) using AS&SH and it runs just fine just superimposing the OSR on the 3rd ed stuff whole-cloth.  My approach is to keep things simple. I don’t bother with formal conversion or worry about any of the ‘splat’.  I’ve simply taken the spirit of a given scene or NPC in SGB and translated it into AS&SH terms.  Because the latter is designed to run S&S, this works just fine IMO.  Any deviation, the players are unlikely to notice (and does it really matter, anyway).  Monsters are easy because there are likely to be OSR equivalents ‘out there’ somewhere, or one just makes them up based on the SGB or 3rd ed source material.  Again, this is not an attempt at a faithful conversion, but rather to get the spirit of what seems to be intended. 

So in a nutshell, running SGB in AS&SH is a piece of cake.  

One thing to note, I use AS&SH rules to run the campaign in Xoth, not Hyperborea (no disrespect to Hyperborea).  Converting across the game world is not something I can comment on.  (That said, I’ve not made a big deal of the wider world because a high level of geographical knowledge is not extant in my interpretation.  I’m seriously considering subtly shifting things to a S&S alternate version of ancient Mesopotamia.  Of course, Thulsa has also written a  module set there too..).