Yes, you can and it is still used to show a fairly weak hand, but it isn’t quite the same as making a 1NT response when the opponents haven’t overcalled. Once the opponents have made a suit overcall you must hold a stopper in that suit if you are going to make a 1NT bid. Also, you will want to be holding 7 to 10 points, whereas without the overcall you would bid 1NT with 6 – 9 points.
Why the increase in minimum points?
Without an overcall we should bid if we hold 6 or more points. Our partner could hold 18 or 19 points and still have made an opening bid of one of a suit. We don’t want to miss a game bid. However, once an overcall has been made, partner will have the opportunity to bid again anyway, so we can pass on a poor hand with 6 points.
Take a look at these examples: