With an 8x10 I would think you would be okay. But the only time I was under it during a storm I was in a hammock so it's not a fair comparison.

The people who use bivies and tarps frequently use a smaller tarp like a 5x8. With the 8x10 it should work without a bivy but it depends on two things. First you need to pitch pretty low to keep any windblown rain out. Second you need to have you tarp oriented correctly to the wind.

Of course the problem there is predicting which way the wind will be blowing at 2am.

One other consideration is your bag. A little spray on a synthetic bag is not an issue. But down bags don't dry quickly and so you want to try harder to keep them dry. If you have down then you'd better use a bivy.