The usage of 五月蝿い in the present day is not cut-and-dry. It is not an entirely abandoned spelling, but how common it is depends on the field.
- Fact 1: Because 蝿 is not in the 常用漢字 list, editors of materials that stick to the list when possible (newspapers, materials for kids + learners, many other "regular" publishers, etc.) will not use it. Now, for some words that involve a mixture of 常用 and non-常用 kanji, publishers will just replace the offending kanji with kana, e.g. 漏えい instead of 漏洩. But because 五月蝿い is ateji as Ken points out, you can't apply that technique very well: the best you could do is 五月さい, but that is not very satisfactory because the 蝿 does not correspond to the さ in any meaningful way, and indeed without the 蝿 as a visual cue many people would probably read that string as ごがつさい and be momentarily confused. So if you can't use 蝿, you may as well just write it うるさい or, less likely, 煩い -- less likely because although 煩 is on the 常用漢字 list, うるさ[い] is not an approved reading for it.
- Fact 2: 五月蝿い is nevertheless a pretty well-known ateji, and so in cases where there is no strict "常用漢字 only!" policy in place, it may be used. It is not uncommon in literature, for example, and as it will usually be offered as a choice by cellphone/computer input methods when you enter うるさい, many people might use it in mail or blogs even if they wouldn't use it writing by hand.
Okay, so first of all, this spelling is not fresh to the word うるさい. The word 五月蝿 /sabahe/ has been around since the Nihonshoki, and has been used to mean "noisy and annoying" since at least the 1100s, according to the 日本国語大辞典. So you had 五月蝿 meaning "flies in month 5", then 五月蝿 meaning "noisy and annoying (like the flies in month 5)", and then finally someone applied the block 五月蝿 to the spelling of うるさい. This may seem like a minor point, but my point is, the spelling 五月蝿 was presumably only invented once, and that a long time ago. It may be the case that the environmental or social conditions that made the flies in month 5 seem particularly annoying disappeared thousands of years ago; it doesn't necessarily correspond to anything in the present day.
Incidentally: Why do I use the weird translation "month 5" above? Well, you have to remember that 五月 in the old (lunar) calender isn't the same as 五月 in the Gregorian calendar. It can overlap a bit with modern May but it more often coincides with June and early July, when it starts getting really hot. I don't know exactly what made ancient Japanese people single out the flies of the fifth month as noteworthy, but it clearly had nothing to do with Golden Week :)
No, I doubt it has anything to do with cicadas. I'm not aware of any evidence that ancient or modern Japanese had trouble telling flies and cicadas apart, so if they'd meant 蝉 they would have written it that way. Also, as noted above the 五月 part doesn't correspond to May.