I have a client who wants this cake with buttercream flowers. Is it possible to do that without them falling off?

yes -- place popsicle sticks in the cake sticking out like stair steps arranged where you want to place the roses of course -- put two side by side if it's a big one -- then disguise the sticks with leaves and tendrils if necessary -- and just like in your picture place the flowers kind of on their side onto the stick -- with their little butts up against the cake --

if those little ones are drop flowers or if they are just little single blossoms - - they can be made in advance and allowed to dry so that you can stick them on with a blob of icing at the last minute -- no worries

rose buds can be piped right onto the surface -- they stick just fine

or you pipe the small blossoms on there fresh too

I use this recipe making flowers as much as a month or 2 ahead for easier handling 

Buttercream for air-dried flowers. 

1/3 cup water

3 Tablespoons meringue powder 

1 & 1/2 cup shortening (Crisco) 

5 - 5 1/2 cups powder sugar 

Sift meringue powder then mix with water beating to a stiff peak.  Add shortening and 5 cups sifted sugar beating on low 3 to 5 minutes til smooth.  Store in air tight container.  Keeps at room temperature for 2-4 weeks.  Once piped flowers are left at room temperature UNcovered to dry several hours to 24 hrs depending on the flower.  Then store them loosely covered in a box.   Will last up to 6 months.  Can flavor as wanted using up to 1 Tablespoon of any  combination 1 to 5 different ones.  

Hope I’m not too late with the suggestion 

I have never used the method K8 suggested.  Just a dot of fresh icing will hold most, then on larger/heavier ones like roses pipe an open circle of b’cream on the back of the flower.  It acts much like a suction cup to help hold the flower on .