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You can use the conditional of plaire but I think it might be quite uncommon since "s'il te plaît" is such a common set expression.
I think I may have come across "si ça te plairait"
Again ,perhaps the "il" in "si'l te plairait" might refer to an actual (male) person rather than an "it" -and might work better then.
No. We don't use conditional mode when saying "please". Never.
"Plairait" is used, but not with the meaning "please".
Il te plairait = You'd really like it.
Je vous remercie, Chantal.