MathWorks has not fully tested executing 32-bit applications compiled with MATLAB Compiler on a 64-bit machine. However, 32-bit application created with it should be able to run in emulation mode. This applies to Windows and UNIX platforms as well.
The process for deploying a 32-bit application onto a 64-bit machine is the same as deploying to a 32-bit machine. Note that you will need to install a 32-bit version of the MATLAB Compiler Runtime (MCR).
A 64-bit distribution of Linux should include 32-bit and 64-bit versions of libc and other libraries, so you should not need to copy any additional libraries to that machine. You can determine all the dependencies of your 32-bit application by using the LDD utility.
If you have the option, it is best to compile your application on the architecture you plan to deploy on, as MathWorks has tested same-architecture combinations more extensively.