You can choose a school when converting, but otherwise no
Btw, Ajam is the better choice compared to QQ..they hold more provinces needed for forming Persia and can easily gain the rest by jumping on Timmy during it's vassals independence war. They are also Sunni, so when forming Persia you get an event for a free switch to Shia, without penalty, allowing you to then choose a school. And they aren't tribal, so you don't need to waste 700 adm to reform. I formed Persia as Ajam in 1450, while QQ needs to wait to tech 8 I think to reform as well, so they eat more AE due to not having the perma claims early
Conclusion: As Ajam->Persia you can have both -shock received and +shock