It is possible to charge it while using Slimport, but that also can depend on which Slimport adapter do you have. I have some Chinese adapter with built-in USB cable, and it is working great...
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~LGE Nexus 5 / Asus Nexus 7~ ROM: Stock KitKat
HTC One X, Samsung Nexus S, HTC Desire, Nokia N97 (black), Nokia 6220c, Nokia E65, SE Xperia X1, Nokia N96, Iphone 3G 8GB, SE P1i, SE W660i, Nokia 7650 (first symbian s60 phone), SE T300i, Motorola V525, Siemens S45i, Nokia 8210, Ericsson T28, Ericsson R320, Nokia 7110 (first wap phone), Nokia 3210, Panasonic GD30...