Yes you can cook spaghetti squash cut side up or the other way around as well.
I've done it both ways as in cooking the spaghetti squash cut side up and cut side down and the spaghetti squash has always turned out just fine either way.
However most people do cook spaghetti squash cut side up for the best results.
Then allow the spaghetti squash to cook in the oven for up to 45 minutes and then it should be fully cooked and ready to eat after you cool it down.
Some people like to cook their spaghetti squash for an hour which is also fine but just be sure to not overcook it and keep an eye on it to be sure it doesn't get burnt.