Should I repot this orchid arrangement while it’s still blooming?

I’d deal with the no drainage without necessarily disturbing the roots right away. If the orchids are sitting directly in the ceramic pot, see if the arrangement can be lifted into a plastic pot with drainage holes, then set that inside the ceramic one. Take it out to water, and let it drain completely before putting it back. Never leave water pooled in the outer pot.

If it’s stable and the roots aren’t staying soggy, you can wait until flowering is done for a fuller repot. Use a loose orchid mix rather than regular potting soil, and keep it in bright, indirect light.

I’d make the call based on what’s happening in the pot, not just the blooms. If it’s wet inside with no way to drain, or roots are soft and rotting, I’d move it into a draining pot now, even if some flowers don’t last as long. If the roots look firm and the planting medium isn’t waterlogged, waiting until the flowers fade is a reasonable way to avoid extra disturbance.

Keep firm roots and trim only roots that are clearly dead or mushy, using clean scissors. Don’t water by a rigid calendar. Check how dry the mix is, water thoroughly, then let all the extra water run out.

Don’t automatically split them. First check whether these are separate plants or a joined cluster, and whether their roots can be separated without a lot of pulling. If they’re tangled together, keeping them as a group in a well-draining pot may be less disruptive. If they come apart easily, individual pots can make watering and checking roots simpler.

For common moth orchids, a chunky orchid bark mix, sometimes with a little moss, gives roots air while holding some moisture. Avoid harsh direct sun, especially if the leaves aren’t used to it.