Yes. CD and SACD use different processors in the player.
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Well, more than that too... some CD/SACD players use different lasers as well. If DSD is a feature then those circuits need be run in too as Red book won't use that path.
I just had a new 'sled' put into my Sony SCD xa777es SACD/CD player. I was amazed by the time it took for the new lasers and drive motor to get settled in. In fact I've not yet allowed the SACD portion to get run in entirely as SACD playback has for me, become far less a priority.
Even once run in, I've noticed some lengthyer times for the SACD section to get warmend up. that's likely due to how little I use it though.
But yeah. they are separate items, if DSD and/or separate lasers are involved. I don't think every CD/SACD player out there uses twin lasers and/or separate DACs though... so check yours out to be sure.