I intend to get a Visa on Arrival at the destination country. In that case, without a visa, will the airlines allow to check-in at the source?
This is possible, but I would recommend bringing proof to the airport that you can get a visa on arrival. I've been in the situation where the person checking me in didn't know I, as an American, could get a visa on arrival to Dubai—which is not a difficult thing at all. Perhaps the computer was down that day; perhaps the person had never worked that route. Whatever the case: bring proof for the sake of the person checking you in, because they need to approve your boarding.
The people at the check-in counter have a database in which entry requirements can be looked up. If the database states that you can get a visa on arrival, they will let you check in. If it does not, they might (in some cases) double-check with the airline or (much more likely) just refuse boarding.
Note that "it is possible to get a visa on arrival" is not exactly the same as "the database says it is possible to get a visa on arrival". For most destinations there should not be a problem, but some countries are not as good at keeping such info up-to-date as others.