Yes. But you can think of it as two separate systems.

So:

• If you have 32-bit Javas, those can only map to 32-bit browsers.
• If you have 64-bit Javas, those can only map to 64-bit browsers.

For instance if you have:

32-bit Java 7 Update 80
32-bit Java 7 Update 95
32-bit Java 6 Update 81

And

64-bit Java 8 Update 121
64-Bit Java 7 Update 99
64-bit Java 7 Update 51

Then you can map 32-bit Javas to the 32-bit browsers you have.

• When running 32-bit IE, www.foo.com –> 32-bit Java 7 U 80.
• When running 32-bit IE www.bar.com –> 32-bit Java 7 U 95.
• When running 64-bit IE www.xyz.com –> 64-bit Java 7 U 99.
• When running 64-bit IE www.pdq.com –> 64-bit Java U 51.