(Native speaker here, only amateur linguist (-: ) Interesting question, linguistically. The short answer is no. In עוגה indeed the stress is on the last syllable, but in גובה="height" the stress is on the first.
But digging deeper, in quickly thinking I found very few words with a final ה that are stressed on the penultimate syllable. And in all those words, the ה is part of the radix. In the vast majority of words ending in ה it's not part of the radix but a suffix. It's possible that any such suffix moves the stress to the last syllable. But I'm not sure that's the best explanation.
To compound the situation, there are some words with final ה that "by the rules" are stressed on the last, but in spoken Hebrew are stressed on the penultimate: כמה, איפה, and many many given names: משה, חנה, שלמה. Might be that the penultimate stress is a left-over from Ashkenazy pronunciation.