I had a play with my shiny new Agilent 33522B, and it is possible to do what you want, using a single channel (so a 33511B would also work).
Set up the ARB waveform with whatever sample rate you want, and select the preferred filter to give you smoothed signal output. Disable modulation & sweep, enable burst. Select burst on, N-cycle mode, #cycles to 1. On the trigger menu, set the source to 'timer', then on the 'trigger setup' menu set the time period to whatever you want. Back on the trigger menu, set Sync on, set the channel to whichever channel you are using. On the 'Sync setup' menu, choose normal or inverted as required. If you choose sync mode 'normal', you get a sync pulse that stays active for the duration of the ARB signal being bursted. If you choose the mode 'carrier', you can adjust the number of samples (at the ARB sample rate) for which the sync signal is active, down to a minimum of 4.
In both cases, the sync pulse starts at the start of the ARB waveform. You can adjust the burst phase to shift this, if your ARB signal starts & ends with a 'guard band' of constant DC level.