It's not really strange to alternate, but it isn't exactly a popular play style either (considering how few people alternate compared to single tapping). I alternate at all times myself, but it wasn't exactly natural. I had to learn how to alternate since I'm ridiculously slow at single tapping. You should use whatever style works for you, in the end it all comes down to preference.
A far more interesting play style is alternating between tablet tap and keyboard key at all times. Black Sheep, TTTL and Amamiya Yuko are some players who play like this. Alternating keyboard is one thing, but alternating like that is just crazy, I simply lack the coordination to do it properly (would love to learn this play style though).