As I know, you can install 32 bit applications on 64 bit system, as long as the machine is not running for resource-intensive environment (e.g. servers).

The only drawback is, system memory (RAM) is not utilized efficiently.. (i.e. two 32 bit words are not stored in one 64 bit word, instead, they consume two 64 bit word spaces with each word-space half empty).

So, it is not good, though there is no apparent issue.