It can, yes. The word "летают" used here is the multi-directional form (like saying "я хожу" instead of "я иду"), so it basically can mean any of the things that multi-directional verbs of motion can mean in Russian. According to this section's explanatory page, this sentence could potentially mean 3 things:
- The pigeons often fly to the park. (Repeated or regular trips rather than just one trip happening right now.)
- The pigeons are making a round-trip journey to the park. (They are somewhere else right now, but are going to the park with the intent of coming back afterwards.)
- The pigeons are flying around inside the park. (They are not making a "trip" with any specific goal in mind, but rather just flying around because that is what pigeons do. Personally, I consider this to be the most likely interpretation.)
As of this writing, you can see the different conjugations of "Летать" and "Лететь" here (this site uses the word "Indefinite" to refer to the multi-directional verb forms, and "Definite" for the unidirectional forms): http://www.russianlessons.net/verbs/35
This is the only Duolingo course that I have take which teaches the word for pigeons. Good on the Russian course creaters. Most people see many more pigeons than elephants. These type of words are more important than people give them credit. You should learn the work bakery and diner in Portuguese before the word for restaurant for example. It is an everyday part of life.
Actually, the word for "elephant" is not particularly rare. Still, using a corpus makes seeing patterns easier. Most common animals mentioned in Russian go about as follows: лев, волк, медведь,орёл, змея, заяц, муха, слон, ворона, ворон, соловей, обезьяна, ёж, олень, тигр, бабочка, голубь, лиса, утка, жук, чайка, пчела, воробей, кролик, лебедь, лягушка, дракон, таракан, крокодил, муравей, кит, сова (apart from the domestic кошка, собака, кот, корова, курица, свинья, козёл, коза and so on).
Words дикий (wild), нора (hole), стая (pack, flock), гнездо (nest) are also pretty useful.
In total there are about a hundred animal names that a native speaker can easily recall (you should also include umbrella terms like птица, животное, жук, рыба etc.).
Because yours would be "Голуби летят в парк." "Летят" is the perfective or unidirectional verb aspect for "are flying."
Голуби летают в парке means that the pigeons are at the park, flying around there, multidirectionally.
Also, "Я лечу в Москву," is what you mean if you're talking about one specific flight to Moscow. If you're talking about on a regular basis or just whenever, unspecified, then it's "Я летаю в Москву."
летают (multi-directional) and летят (unidirectional) are imperfective. There's no perfective present tense conjugation in Russian, so both of them can be translated as "are flying" (which is accepted now).
летят is not out-of-the question. If there's a homing-pigeon race that starts in the park, on release the pigeons would indeed fly unidirectionally home.
That would be especially applicable if the translation is "The pigeons are flying in the park", because the sentence addresses a particular group of specific pigeons.
If the sentence is simply talking about wild pigeons flying around the park, then the translation should be "Pigeons are flying in the park".
"The pigeons fly in the park" is actually a strange sentence in English. It's somewhat ambiguous and a bit confusing.
I'm not arguing against the teaching of the word elephant. I am simply applauding the creators of the Russian course for including the word pidgeon. It is a very common animal in a large part of the world and is most often underrepresented in language learning. Good job for including them.
Both are correct. The difference between the two, in Russian, is determined by context. There is no difference in Russian between "are flying" and "fly." The context could be:
Голуби летают в парке летом. --"Pigeons fly in the park in the summer."
Смотри! Голуби летают в парке! --"Look! The pigeons are flying in the park!"