Could SQL server 2008 R2 instance “sustain” OS upgrade from Standard to Enterprise?

Has anybody ever faced such issue – a necessity to upgrade Win2K8 R2 server from Standard to Enterprise while keeping the installed instance of SQL Server “untouched”? What we have is SQL Server 2008 R2 Enterprise edition installed on top of Win2K8 R2 server (Standard). Currently the SQL database is limited to 32GB of RAM due to licensing constraints, and we need to upgrade the server to 2008 R2 Enterprise to triple the memory space. Is it possible to perform such upgrade without rebuilding the SQL installation from scratch – as far as it’s production environment we’re really limited in possibilities to downtime the SQL server running?

Thanks in advance