Downloads de Java para todos os sistemas operacionais afirma:
If you use 32-bit and 64-bit browsers interchangeably, you will need to install both 32-bit and 64-bit Java in order to have the Java plug-in for both browsers.
De acordo com Instalação do JRE em computadores Windows de 64 bits :
64-bit Windows operating systems (which may be Windows 7, Vista or XP) come with a 32-bit Internet Explorer (IE) browser as the standard (default) for viewing web pages. These operating systems also include a 64-bit Internet Explorer browser. However, using it is optional, and it must be explicitly selected to view web pages. Note that because some web content may not work properly in a 64-bit browser, it is recommended that you use the default 32-bit browser and install the 32-bit JRE.
De acordo com Instalação do JRE para Microsoft Windows (64 bits) e Qual download Java devo escolher para meu sistema operacional Windows de 64 bits? :
The following are some of the known issues when you install a 32 -bit JRE on a 64- bit Windows architecture machine:
Online Installation and Java Update features are not applicable to 64-bit architecture. This means that you will not see an Update tab as part of the Java Control Panel. You can manually update Java on 64-bit Windows by running the latest Java 64-bit offline installer.
The public JRE installed with the 32-bit JRE is not registered. You must set the PATH environment variable to point to JAVA_HOME \bin to register the JRE.
Portanto, sim, exceto pelos problemas mencionados acima, o JRE de 32 bits também funcionará bem nas versões de 64 bits do Windows, contanto que os navegadores de 64 bits não estejam sendo usados.