To add to the personal experience, I've spent a lot of time on English keyboards not knowing the tricks to do accents under Linux and writing to French people or participating on French forums. All very informal contexts. I did get people complaining and pleading with me to get some accents already.
It can get wearing to read unaccented French, because a lot of common words are distinguished only by their accents - où/ou, à/a, conjugations of verbs of the first group... It makes it an extra effort to parse the text, like when someone makes lots of spelling mistakes. If the person is likely to make language mistakes on top of that it might get downright hard to understand.
I'd say that you "can" do it, in that you won't be the first or last person to do it and plenty of people won't care, but some will.
(to add to the ASCII codes info, if you don't want to write them down or memorize them, know that they follow a specific pattern. Knowing it you can find the correct letter in a few tries, and over time you can end up learning the codes that way.)