My gyno told me I could do this, but that I would have to take the placebo pills once every 3 months to get a period and "flush" my system. I tried doing it in the past and it didn't work for me. On the week when I was supposed to get my period I didn't bleed, but I still felt like I had my period if that makes sense. Basically, I still got all of the symptoms except for bleeding. Also, the feeling of having my period lasted and got even worse the next month like it was building up. The feeling didn't go away until finally I had my period on the third month and I decided to never skip anymore periods lol. So I guess for some people it works and for others it doesn't.
I recommend you read this blog about whether never having monthly periods is healthy or not.
Then decide for yourself...there are opinions on both sides.