Well, yes and no.
In one sense, qualifications and impediments are regulated in universal canon law even though proper law makes those additional specifications as you note correctly. It’s just that they’re mixed in with other conditions in the code and are thus easily missed.
Canon 597§1. Any Catholic, endowed with a right intention, who has the qualities required by universal and proper law and who is not prevented by any impediment can be admitted to an institute of consecrated life.
See canon 642 on qualities.
See canons 643 for the five impediments of universal law to entering noviate validly: §1. One is invalidly admitted to the novitiate: 1º who has not yet completed the seventeenth year of age; 2º who is a spouse, during a marriage; 3º who is presently held by a sacred bond with any institute of consecrated life or who is incorporated in any society of apostolic life, with due regard for the prescription of can. 684; 4º who enters the institute as a result of force, grave fear or fraud, or whom the superior receives induced in the same way; 5º who has concealed his or her incorporation in any institute of consecrated life or society of apostolic life. §2. Proper law can establish other impediments to admission, even for validity, or can add other conditions.
Valid noviate is a requirement for valid temporary profession in canon 656 and see canon 658.