My question is : Can I install the Vmware Update Manager on the first server (adapting RAM) and linked the VUM to the SQL Server database on the second one (using ODBC source) ?
Yes, you can. You are free to install VUM on either of the two systems, or even on a completely new different system if you want to. You specify the appropriate DB/ODBC and vCenter server during the setup and VUM will point to them. It doesn't matter where the components are installed as long as the systems can communicate with each other over the corresponding network ports.