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..ha, nice - they look happy for under-desk plants : ]
The thing with flowers, as far as my understanding goes, is just that the plant will put like 90% of energy into creating those (instead of building more branches, roots, etc.) - which actually may be just fine given your circumstances (it sounded like your idea is just to tide them over the winter until next spring / summer, not to grow huge plants under your desk).
On the other hand plants will drop the flowers when they realize they don't get enough energy (from sun / from soil) to then grow the actual berries - so it might result in a wasted effort - but long story short I would just leave one or two flowers and cut off the rest if there's more..
1 month later. I've added an ikea plant bulb hooked up to a timer for a daily dose of sun.
They are going rather well - infact 1 is trying to grow flowers - how would people deal with this? Simply cut back new branches until spring?