While you will be pushed to implement a universal phonetic alphabet, it will usually be possible, especially when an extended character set is available (using the option or alt key and sometimes key sequences), to find enough mnemonically appropriate characters to satisfy the requirements at least of one language at a time. (Mac users will find that option b provides a good approximation to the IPA symbol for a voiceless palato-alveolar fricative in most fonts.)
But be warned. You need to watch out for potential clashes with characters which have a special status in the programming language. Although [ and ] may have enough similarity to the IPA symbols for a pair of mid-open front and mid-open back vowels to make them candidates for transcribing say pot as p]t and bed as b[d, you would immediately fall foul of their use in Logo to mark the beginning and ends of lists.
It does not follow, however, that, at the point of user input, sequences of characters cannot be used. As long as some pre-processing of an input string converts character sequences where necessary to single character equivalents before the string is passed on, the basic procedures can continue to be defined simply. And it does not matter to them whether the single characters arrived at in the re-coding have mnemonic value or not. If the pre-processor translates the digraph ch (which you might not unreasonably use for the first consonant of chips) into the number 4, the Logo interpreter is not going to bat an eyelid.
Naturally you will need to select with great care the character sequences which you will use to represent single segments. If you think that th is a nice way to handle the dental fricative at the beginning of think (because it matches the orthographic convention) then what about fathead, fathead?
On top of these problems you then have to implement the pre-processor and you will no doubt find that its manipulations slow down the overall processing time. But the trade-off may be worth while. Look here for a simple example of a digraph pre-processor.
The problem of undecipherable Logo code disappears, of course, if separate user input and display windows can be opened, but clashes with special symbols can only be dealt with by careful selection of a font. Of the freeware Macintosh fonts I most often use, PalPhon seems to work more easily with LogoPLUS - for my purposes - than SIL IPA or TechPhonetic. Click here for a page of links to sites holding phonetic fonts.