It is good that you are wary of this, but A260/230 & 260/230 imbalances are not always a problem depending on the application. If you are thinking of doing array experiments, a high 260/230 ratio could mean increase in background/noise. If you are doing real time PCR with enzymes that are resistant to inhibition, you shouldn't be adversely effected. So you should ask, would my application be affected adversely by this type of sample. If you are doing in a PCR, it's not a big deal if it turns out the sample was inhibited or behaved strangely - PCR is cheap and fast. But for NGS and array sample, the story it different - you could stand to lose an array which could be costly. So the answer to your question depends on the application and the requirements of that application which you should be able to find out.
Compare the amplification of samples like this to other more pure samples. If they cluster tightly around the same Ct (assuming same group, same RNA and cDNA input), and the curve looks exponential, then it's most likely OK. I've also done real time for microRNA applications using SYBR green chemistry, was OK for me. You can check for inhibition by making dilution series, 1:10 would be ok especially if there's an abundant microRNA. See if you can find anything that has a Ct of 20-21 ish, with that you can make 1:10 dilutions (5-6 of them) or you could even check with 1:2 (half-half) dilution if your microRNAs amplify late (around after 30-33 Cts roughly). If you do 1:2 dilutions (that is half diluent half cDNA), remember your Cts will differ by roughly 1 (i.e. take 1:20 cDNA, make it 1:40, then 1:80 etc). So in the above case, if 1:20 came out at 25 ct, then the 1:40 should come at 26 Ct if amplification efficiency is near 100%. If you generate a 5-6 dilution series, you can get an idea if there is inhibition. I hope that makes sense to you.