Java Downloads for All Operating Systems states:
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.
As per Installation of JRE on 64-Bit Windows Computers:
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.
According to JRE Installation for Microsoft Windows (64-bit) and Which Java download should I choose for my 64-bit Windows operating system?:
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.
So yes, except for the issues noted above 32-bit JRE will work fine on 64-bit Windows versions as well, as long as 64-bit browsers are not being used.