No they can't, assault rifles are made for a male build and strength, women have significantly harder time using them. I was in the military and the women had a really hard time passing the basic tests for assault rifles since they had shorter arms and weaker upper body strength.
Can women do it with training? Yes, but basically every man can do it without training, I've seen it myself. And if those women doesn't keep up that strength as civilians they wont be able to use the assault rifle properly if they need to.
Edit: As for being smaller, being able to wear body armor is more important. Level 3 body armor is standard for combat situations and that is heavy, ammunition is also very heavy. Typical combat gear is about 20-30kg in total, that is heavy even for men and untrained men get significantly slower from it but they can still operate. That is for a basic infantryman with just combat equipment, no food or anything, that is the minimum to fight.
