In many cases, yes. I cannot give you a definitive answer as there are many different portable devices, and no one hard level standard. If you would like to know how to solve without marking, then perhaps you could post an example as a response, and if it is possible, someone should be able to let you know how.
You may be also interested to know that solving the puzzles without marking has also been discussed in other threads, eg
http://forum.enjoysudoku.com/viewtopic.php?t=3087.