What a great question! It may be that the poet is thinking of only himself when he writes that his subject will live, forever beautiful, within the lines of his immortal poetry; then again, it may be that he truly meant what he said at the time--that the "beauty" is his sole focus and that to him, the physical beauty of this person will forever remain alive no matter what happens to their relationship, their lives, their bodies after death. Which is more important? The target of that love or the poem and the poet's vanity? That is the question. With every question, however, there are exceptions. The same answer will not be true for every poet who claims that someone will live on forever within the lines of his poetic creation. Each case will be slightly different, methinks.
I like the question very much! I have always felt there was a certain cocky self-assurance to many of WS's sonnets. He ends several of them by saying, "I think this poem is of immortal quality, unlike you my love, it will beat death and live forever. 'Cos I'm a genius and you ain't." But he was right of course! We don't even know who that 'beauty' was, now dead for centuries, but the poet and his poems endure.
As for 'the artist trumping his subject', I love this poem by Shelley. It talks of a great emperor of ancient Egypt, Ozymandias. The only thing that remains of Ozymandias and his powerful empire is one broken statue. And on the face of that statue you can see that the artiist thought Ozymandias was a cruel and stupid man. All that remains of the king, the artist or the empire is the artist's 'beauty and truth'.
I met a traveller from an antique land
Who said: Two vast and trunkless legs of stone
Stand in the desert. Near them on the sand,
Half sunk, a shatter'd visage lies, whose frown
And wrinkled lip and sneer of cold command
Tell that its sculptor well those passions read
Which yet survive, stamp'd on these lifeless things,
The hand that mock'd them and the heart that fed.
And on the pedestal these words appear:
"My name is Ozymandias, king of kings:
Look on my works, ye Mighty, and despair!"
Nothing beside remains: round the decay
Of that colossal wreck, boundless and bare,
The lone and level sands stretch far away.