Yes you could place an absolute element at the bottom of a container or background image and in some circumstances that would be fine.
As usual with CSS it depends on the context and what comes next. If you had lots of text then it may not fit within its relative container and overflow the page. If it's just a couple of words on one line then you can probably accommodate it easily enough.
Adding duplicate content to hold the page open is of course a bad practice and bad for seo and could get you marked down especially as you have hidden the text. I would have just padded out the container to preserve the absolute element.
Absolute positioning is fine in small doses but when you have unknown amounts of text then its best to find a more robust solution that won't break if someone resizes the text or your cms outputs too many lines.
In the end it all depends on context so sometimes absolute positioning is a good answer and sometimes its not.
One of the key things I've learned is always to say "What IF?"
What if there are ten lines of text.
What if the image is smaller
What if the user uses text zoom only.
What if an unbroken word is longer that the space I allocated.
What if images don't load.
Why is 750px min-height the answer?
and so on ....