What would be the status of a distance-learning Master's program in academia? Would it fulfill the requirement of an on-campus Ph.D. program?
What would be the status of a distantce-learning doctoral program in academia? Would it be considered on par with an on-campus Ph.D. program?
To answer the question literally: Yes, I know for sure that it is possible, because I have done it. I've studied Computer Science at the FernUniversitaet Hagen (https://www.fernuni-hagen.de/), the leading German distance-learning university. I got my BSc and MSc from them, before being admitted for a PhD at the University of Cambridge. At no point during the admissions process to Cambridge (nor when it came to later job applications) did I feel that the distance-learning nature of my prior degrees was held against me.
Whether it would all work out just fine for you is subject to two caveats: First, whenever you are doing something in an unusual way there is a certain risk that the specific decision makers you encounter are put off by this, and have it count against you. Second, I'd reckon that there are more "bad apples" amongst distance-learning universities than amongst in-person ones. So you'd want to be sure that you are dealing with a reputable programme/university.
"Fully online masters/doctoral program" is too broad to make a general statement. It would depend on who runs the program and how it is run.
And the formal answer to the topline question is yes, you can enroll if you are admitted, but the judgements of others will be required to make it possible, just as in any other case. One doesn't just "enroll". One must be admitted.
Moreover, it is individuals who make such decisions and there are no general rules about the equivalence or non-equivalence. But, I think most people would be skeptical, as I would be, and would want to see some details about any such program.
Certainly there are reputable universities running reputable programs. In UK, I'm only familiar with Open University, which I believe does a very good job and has a history of success.
But the issue that many would have is how much actual learning has taken place in online programs and how much can claims be depended on in making decisions such as employment and further education.
Personally, I worry about such programs due to the possible reduced interaction, especially personal feedback, between students and faculty. I'd be especially skeptical of anything of a massive nature. It is possible to run such programs with a student faculty ratio of 1000/1, of course and my trust in such a program is about 1/1000. It is also possible to serve a large number of students in a "class" but with a ratio of 20/1 as is done in some Harvard programs (800 students, 40 staff, though only one professor). This is hugely different.
The "status" is actually undefined and will be judged by whoever is in a position to have to make a judgement. This will probably remain true for some years until there is better overall information about the long term outcomes of students who have done these programs.
Certainly one can learn in an online program, but it is harder to judge whether someone actually has, given the possibility of much-reduced interaction and evaluation.
If you intend to do such a program, look first at the student-staff ratio and at how much feedback you are likely to get in the program and how easy or difficult it will be to get good answers to your questions along the way. Of course, the same can be true of face to face programs. The second thing I would look at is whether the program has found a way to encourage active learning. If the system is too passive (videos and exams primarily) then I would personally judge it to be of low quality. If it requires fairly extensive writing or other exercises and personalized feedback then it is (IMO) likely to be of higher quality.
Note that I've taught both ways. Nothing massive in the online world, but small groups who met face to face only rarely and who had essentially constant opportunity for internet mediated group conversations and contact with faculty. That can work.
