That was only true for 4870 cards because they didn't downclock the GDDR5 memory at idle because it would briefly cause on-screen corruption when the memory clock changed. That wasn't a problem with the 4850 because it used GDDR3 (and one card from Sapphire used GDDR4) which could downclock.
I have a VisionTek (reference) HD4850 512MB (I think GDDR3?) card in my other box, running DC. My understanding is that even the DDR3 cards still had pretty high idle power.
ZeroCore was a feature of newer AMD cards, and was not present on the older 4xxx series.
Try to pick up a cheap 5450 card, if it's just for display output. I think Newegg has one in their BF sale for $20 with a $10 rebate. That, or a cheap GT610 AR. Both cards are very entry-level, and are even eclipsed by newer APUs/IGPs.
Truth be told, repurposing older gear always seems to have a cost, as far as power-consumption goes. If you really care that much about it, a cheap FM2/FM2+ micro-ATX board, with SATA 6G and USB 3.0, can be had for $50 or so, and then drop in a dual-core AMD APU with a half-decent IGP on-die, and some cheap DDR3, and a cheap SSD (possibly refurbed if you go that way), and she would have a power-sipping rig, instead of a hand-me-down gaming rig outdated monster.