No, in short. But this is one of those cases where grammarians hedge. The big Quirk grammar says, at the relevant point (5.59) 'The conditions under which a/an occurs in such cases are unclear'.
Indeed they are. One of the problems is that many nouns in English can be either countable or uncountable, as in cake/a cake, coffee/a coffee, a tobacco (meaning 'a type of tobacco'), and so on. Here we are talking about nouns which are rarely if ever thought of as countable.
Quirk et al say two factors are relevant. Fist, there's likely to be a personal theme. The noun must refer to a quality or other abstraction which is attributed to a person. One of their examples is:
Mavis had a good education.
Nothing wrong with that. And we can talk about such qualities as annoyance, togetherness, and generosity in this way:
The late arrival of the train was a real annoyance.
John and Mary display a charming togetherness.
That's what I call a generosity of spirit.
But we can't do this with, say, progress, heraldry, and shoplifting:
*We made an important progress.
*I looked at an interesting heraldry.
*That was a shoplifting I disapprove of.
The other point Quirk et al make is that, the greater the amount of premodification or postmodification, the more likely we will find the indefinite article. So, to develop their example:
She played the oboe with sensitivity.
*She played the oboe with a sensitivity.
She played the oboe with a great sensitivity.
She played the oboe with a great and engaging sensitivity.
She played the oboe with a sensitivity that delighted the critics.
She played the oboe with a great and engaging sensitivity that delighted the critics.
The more we pre/postmodify, the more we allow the particularising function of the indefinite article to operate.
Having said all that, I'm not entirely sure which uncountables follow these trends. The semantic criterion (personal attribution) is inevitably a bit fuzzy. Is plagiarism included, for example? Would you accept The teacher discovered a fresh plagiarism? I think there might be quite a lot of divided usage here.