Not really. That would require the conditional mood for the main verb in Romanian: Ţi-ar plăcea să rămâi? (or equally (Tu) ai dori să rămâi?), whereas here the indicative is used (doreşti).
Feel free to ask if you have any more questions.
In English the two sentences "Do you want to stay?" and "Would you like to stay" have the same meaning, and would therefore seem equally valid translations, though to my ear "Would you like to stay" is very slightly more polite / perhaps a little more formal. If there is a difference in meaning (as opposed to grammar) in Romanian it would be good to understand.
I think the difference is the same as in English: with the conditional it's more polite. Such aspects are part of the meaning, too.