No, you cannot file RTI to ICSE as it is not a public authority which comes under the purview of section 2(h) of the RTI Act 2005.
You can file for RTI to public authorities which come under section 2(h) of the RTI Act 2005:
(h) "public authority" means any authority or body or institution of self-government established or constituted—
(a) by or under the Constitution;
(b) by any other law made by Parliament;
(c) by any other law made by State Legislature;
(d) by notification issued or order made by the appropriate Government, and includes any—
(i) body owned, controlled or substantially financed;
(ii) non-Government organisation substantially financed, directly or indirectly by funds provided by the appropriate Government;