I’m going to say ‘no’. But before answering your challenge to saying 'no', a comment on your challenge to saying ‘yes’. You assume that in order to know that all beautiful paintings are good paintings, I must view all beautiful paintings. But this assumes, in turn, that the only way we can establish a connection between being beautiful and being good is through repeated experience, i.e. empirically. That’s not, I think, true. There could be – indeed, I think there is – a conceptual connection between beauty and aesthetic goodness. Compare: to know that all vixens are foxes, I don’t need to find all the vixens in the world, and check that they are foxes. I just need to understand the word ‘vixen’, meaning ‘female fox’. So if we could show that ‘beauty’ is, conceptually, a type of aesthetic goodness, a standard of what is good, aesthetically speaking, then we can know – without checking – that all beautiful paintings will be good.
But I’m not satisfied with this answer. Beauty is one kind of aesthetic good, but perhaps there are others. Maybe to be good as a painting, i.e. a work of art, requires something either different from, or in addition to, beauty. I think it does. And knowing what makes a painting a good painting – knowing the standard for good art - will help us know how to discover whether something is good art or not. This might not be foolproof, or give clear answers every time. That's not an objection. Compare: I can say, perfectly well, how I can judge that there is a table in front of me – I see it – without claiming that my vision is always correct, never confused (think of fog and bad lighting).
So – this next bit is very contentious! Art is about the communication of thought and feeling. Tolstoy (‘What is art?’) says “Art is a human activity consisting in this, that one man consciously by means of certain external signs, hands onto others feelings he has lived through, and that others are infected by those feelings and also experience them.” There are lots of problems with this at it stands, but I think the kernel is right. To judge a piece of art as good or not, we must first understand it, and we should judge it in light of what we come to understand. We need to understand what the artist is trying to do, and then experience that effect ourselves. The first part covers their psychological processes, both conscious and unconscious, but also the artistic conventions and climate of their time (e.g. aesthetic conventions, systems of symbolism, available modes of production, the original purpose of the work, and much else). What you know will make a difference to what you perceive, just as a bird-spotter can see and distinguish different species when the uninformed will just see birds. With this deeper understanding, we can see what succeeds in the painting and what does not, what the artist is aiming at. We can also understand the profundity (or not) of what is expressed there. Some conceptual art, for instance, is gimmicky – once you get the idea, the artwork quickly loses interest. But it needn’t be, e.g. there can be much to reflect on in the way in which the concept is expressed through the medium.
Some beautiful works of art can be relatively superficial, e.g. they may express a superficial emotion (‘isn’t it lovely?’) or view of life, leaving us wondering dissatisfied with it as art, even if we admire the way it looks on the surface. So not all beautiful paintings are good paintings. To know whether they are, I’d need to know much more about the painting and the context of its creation, and then see whether the painting succeeds in communicating what the artist aimed at.