Since Florida is a paid when paid state, if the GC says they have not been funded, can we really send them an NOI obligating them to pay when they haven’t been funded?
Florida does not have a "notice of intent to lien." You have a notice to owner (NTO), due to be served on the owner within 45 days of your first work on the site, and then you have 90 days from your last work to file a lien. The pay-when-paid language only protects the GC. It does not protect the owner. Alternatively, if this is a bonded job, the pay-when-paid clause does not protect the surety (unless it's a conditional payment bond, which it will say on the face of the bond if that's the case). Whatever you do, send the NTO if it's not already too late, and do not let the 90 day period pass without filing your lien (or sending notice of nonpayment to the surety). Let the GC complain all day about not getting paid. Once your 90-day deadline passes, your lien/bond rights are lost and you will be waiting at the back of the lien to get paid.
Florida courts have held that the public policy of ensuring payment of construction participants of all tiers is not as strong as the public policy of allowing freedom of contract. This means, that, like you said, if the proper words are used in the contract such that a clause is sufficiently explicit, pay when paid / pay if paid clauses can be valid. The language requirements are fairly strict, however, so it may be that a contract purporting to be pay when paid / pay if paid may not actually be so.
Florida does not have a statutorily required Notice of Intent to Lien document. While there are preliminary notices that may be required on Florida projects, any notice of intent sent by a party is completely voluntary. Accordingly, an NOI does not obligate the GC to pay whether or not the project's contract is subject to pay when or pay if paid provisions. In Florida, a notice of intent to lien functions like a demand letter or other attempt to get paid, not a statutory part of the lien requirements.
Note, however, that Florida does not allow lien rights to be waived by contract. And, even on projects with an enforceable pay when paid or pay if paid clause, a sub-tier party can still file a lien or make a claim on a bond.
First, it depends on your contract. Florida is only a pay when paid state if your contract with the GC says that. Second, there is no such thing under Florida's construction lien law as a notice of intent to lien. If you send a notice of intent, it isn't any different than sending a demand letter.
That being said, a pay when paid provision does not eliminate your construction lien rights. So, make sure you've sent a notice to owner and otherwise complied with Florida's construction lien law to preserve your rights to payment.