Both are similar so yes it can 100% cause anxiety. Do you know what HMG actually is? How it was derived from the urine of postmenopausal women. HCG is very similar and basically comes from pregnant women (placenta releasing HCG into the blood and urine). So yes if you get anxiety from one you could from the other.
Anyone who is sensitive to anxiety could potentially have issues from adding in anything new especially drugs that affect various hormones. HMG can increase E2, FSH, LH, dehidroepioandrostenodione, androstenodione, and testosterone so if you are sensitive to hormonal changes you have to be careful when adding it in.