Yes. It is easy to tell when it happens, though, and it is also easily correctable. First you get a dizzy feeling. Then you get hot. Then you get all sweaty and start getting confused.
Unless you injected some insane amount, though, it is very easy to correct. I have never been over 20 iu at once, so I can't say anything about those levels, but under that, just drink something sugary. My preference now are those little Dole pineapple juice cans (do not need to be refrigerated and easy to carry). If I misjudge my carbs (and the same carbs are not always enough every time, it is just not the way the body works, you are more insulin sensitive at some times than others), and I feel it coming on, then one of those little cans usually corrects it.
For 5 hours after injecting R, I keep within reach one or two of those pineapple juice cans and glucose tabs from the diabetic section of the pharmacy. It does not matter how much I have to eat. I keep those nearby. I usually do not need them, but at least I know if I start to go hypo in a bad way, I do not need to be going looking for them while in a confused state.
Also, it takes a while. When using R, it comes on slowly. My very first "scare" years ago, I had to go walk over to a fast food place and purchase a large sweet tea. There was a line. I was already drenched in sweat, dizzy, and somewhat confused, but several minutes later had my tea and drank it. A few minutes later, I was good to go.
Nowadays a couple glucose tabs at the first sign of dizziness, and, if it continues, down a pineapple juice, and I am right as rain two or three minutes later. I am much better about targeting my insulin use to my diet, now, however, so I don't really "need" these things now so much as keep them nearby in case of need.