Detecting I/Q imbalance
Yes!

What is done in practice is simply disconnecting (or even better, terminating properly) the RF input of the receiver. 

Then, you observe empiric noise variance separately on I and Q, and normalize so that they are equal.

This assumes that NF variations are benign, but it does work. If you can, you'd of course try to increase noise power.

USRP transceiver daughterboards can be RX IQ imbalance calibrated by letting TX transmit pseudowhite noise at a slight frequency offset (to average out potential TX imbalance) and observing the intra-board crosstalk. Same would work for any sufficiently random external signal. If you have a dominant external signal, intentionally tune a bit off, and average enough.