Hi TOM95,
Yes, you can install either the 32 bit version or 64 bit version and use the same key to activate.
If you want to change over from 32 bit to 64 bit, you have to necessarily do a clean install and therefore activate your Windows afresh.
If you had purchased a genuine Windows retail / OEM system builder pack, you should have no problems activating Windows on the same machine any number of times - but too frequent activations in a short period may necessitate a phone activation.
Having said that, if you want to try the 64bit, you can install and use it for one month without activating it. That should give you enough time to decide whether you will continue with it or change back to 32 bit.
If you want to avoid a fresh activation if you decide to go back to 32bit, you can take an image of your 32 bit installation, save it to an external media and restore it anytime later. No fresh activation wil be required.
There are also programs that can backup and restore the present activation only (without imaging the whole system drive) but you may have to do a google search on your own. ( IMO, restoring the whole system image with activation data or backing up and restoring only the activation data makes no difference as long as one has a legally valid licence and takes the backup and restores it on the same machine.)