* If you mean a high school diploma or equivalent (GED): Generally, no. Most colleges and universities require a high school diploma or GED as a prerequisite for admission to degree programs. There are some exceptions, such as individuals who have demonstrated exceptional talent or experience, but these are rare.
* If you mean a diploma from a previous educational institution: Yes. Many people earn a degree *after* completing other diplomas or certificates. For example, someone might earn a nursing diploma and then go on to get a Bachelor of Science in Nursing (BSN). In this case, the earlier diploma is a stepping stone, not a barrier, to the degree.
In short, a high school diploma or equivalent is usually a prerequisite for a degree. However, possessing other diplomas doesn't prevent you from getting a degree; it might even help.