Without trying to sound like 'Gardeners' question time' rather than 'Fortean times gardening time',I'd say that,yes,plants can produce roots and flowers at the same time,BUT,if you are wanting a CUTTING to root successfully,then I'd recommend removing any flowers and flower buds and any excessive leaves(plants lose moisture through leaves,and without the supporting roots to take up sufficient water,they just can't cope).
Hormone rooting powder is handy,though not strictly essential(just follow instructions on the can),I'd advise covering newly rooted cuttings with a plastic bag to retain moisture for a couple of weeks until roots are growing.
I'd suggest a 'John Innes' number 1 compost as a suitable cutting medium.
Hope this helps.