What is this plant?
Thank you for attaching the images of your mystery plants. they are common purslane (Portulaca oleracea), warm-season annuals. No, you do not want them in your garden beds.
Fortunately, they are very easy to pull out at any life stage as they have a central tap root. (A worthy guideline is this: The sooner, the better.) Gather the "branches" together, grasp at the center of the plant, and gently pull straight up.
See "Common Purslane" - http://ipm.ucanr.edu/PMG/PESTNOTES/pn7461.html