in theory algae is more resilient than plants so if it kills the algae then it would definatly kill the plants.
just my theory though, never tried this in practice.
why dont you transfer your tank to the bath (when the misses isn't in!!) and use just off the boil water to clean the tank. obviously with the plants out. remove and algae infested leaves from the plants as well. while your at it trim the roots down to 1.5 inches. this will encourage regrowth.
that should kill off the majority of algae, then when resetup the plants should be able to outcompete any remaining algae to get you back on track.
i have dont this once and it worked for me but you will need to have good light and co2 for the plants to make a significant impact on algae reduction.