Not necessarily, if your back pain is caused by your breasts. Imagine wearing a school backpack on your chest all day every day, and how that would strain your back and shoulders. Then try wearing a hiking backpack instead with a hip belt. It redirects where the weight is resting on your body. The average women’s corset in the 1800s was strengthened with paper or cording or sometimes whale balleen, a material similar to heat sensitive plastic, which are not really materials rigid enough to limit your movement much. Historical corsets were designed to redistribute the weight of breasts to the hips, for most women it was meant to provide support to the breasts first and foremost, and smoothing a tummy roll or giving a smidge more definition in the waist was just a bonus. Working women who wore corsets in kitchens and laundries and schools or farms had no issues with weaker core muscles.