yes, but if they are used regularly (rather than infrequently) then the cable life tends to be a bit less than it would be otherwise; many such levers cause scuffing of the cable.
BTW if the old STIs are a model that was launched pre 2008 then they will have slightly shorter cable pull than modern (post 2008 launch) STIs such as the Tiagra ones (if they are 4600 or 4700). In theory the interrupters ought to vary similarly but I'm not sure that the manufacturers make two different versions.
cheers