I am manipulating some
my.lt = as.POSIXlt("2010-01-09 22:00:00")
new.lt = my.lt + 3600
#  "2010-01-09 23:00:00 EST"
#  "POSIXct" "POSIXt"
Short answer: No
POSIXlt objects are two specific types of the more general
POSIXt class (not in a strictly object oriented inheritance sense, but in a quasi-object oriented implementation sense). Code freely switches between these. When you add to a
POSIXlt object, the actual function used is
+.POSIXt, not one specifically for
POSIXlt. Inside this function, the argument is converted into a
POSIXct and then dealt with (added to).
POSIXct is the number of seconds from a specific date and time.
POSIXlt is a list of date parts (seconds, minutes, hours, day of month, month, year, day of week, day of year, DST info) so adding to that directly doesn't make any sense. Converting it to a number of seconds (
POSIXct) and adding to that does make sense.