I bill via Paypal (only) and the Paypal system actually handles all conversions automatically for me. I'm assuming it would work the same way for you.
Because I'm in the States I don't have a solid personal opinion on this, but it seems like it would be kind of a pain to have to check conversion rates every billing period...or, technically, daily - because if the rate is higher or lower on any given day you want to make sure you're billing accurately.
If you're concerned about helping your clients and potential clients determine how much they're paying what about installing a
widget like this on your site?