No, biceps development does not affect height.
In other words, the size or strength of your biceps muscles has no impact on how tall you grow or whether your growth plates close. Height is primarily determined by genetics, nutrition, and hormonal factors, particularly during childhood and adolescence. Biceps size is a function of muscle development, which is influenced by exercise and diet, and is unrelated to the skeletal growth processes that determine height.
Your height is primarily determined by the growth of your spinal column and long bones, influenced by hormones like growth hormone. While lifting heavy weights incorrectly, particularly those that compress the spine, might theoretically pose a risk to growth in young individuals whose growth plates haven't yet fused (typically through adolescence), this is more related to the impact on the spine and neck than the biceps themselves. Focusing solely on biceps exercises poses no threat to height.