Yes they will. The constitution mandates it. "Shall call a convention". That's why this works to restore libety, it cuts Washington out of the process.
Never happen.
When the 14th Amendment was being proposed it failed to get the required two thirds majority in the Senate. The Republicans, who had a simple majority, then voted to expel a Senator from New Jersey who had voted against it. The Constitution requires a two thirds majority to expel a member of the house or Senate, but the Republicans said they weren't expelling him, they were just retroactively unseating him and he was kicked out. The 14th Amendment then passed the Senate by a single vote and was submitted to the states - even though the constitution requires a two thirds vote.
The point is the Congress can simply redefine the language any way they choose in order to get out of having to call a convention. They can, for example, define the Congress itself as the convention and then do as they please. And if push comes to shove they'll just ignore the constitution - they do that every day don't they? Congress will never call a real constitutional convention.
It's probably a good thing that there cannot be a real constitutional convention. It would undoubtedly be packed with the kinds of people who spend their entire lives hovering around government anyway. We'd end up with a new bill of rights giving everyone a right to a house, a free doctor, a college degree, and anything else you can think of. But any measure of freedom to resist the government would be gone.