Does a RF frequency multiplier work with ultrashort pulse?
There are dozens of different multiplier technologies that vary in linearity, frequency output, input , harmonic, harmonic rejection.  

Do the math and then define what you need for harmonic levels below the desired harmonic then see what multipliers will perform what you need.

The technmology varies from active diodes, Schottkey didoes, pin diodes, balanced mixers, MEMs and other diode bridge structures with filters with a vary wide variation in price and quality.

But multiplying a 100MHz sine with a 50 ns square pulse is basically a synchronous 50 Ohm switch for 5 cycles.  A square pulse can be considered x1