Realistically the Klingons would be hard pushed to beat the Federation in a full scale war. The Federation has considerably more ship and resources at its disposal than the Klingon Empire does.
Grated the cloaking device gives the klingons a tactical advantage but one that without they stand little hope of victory and starfleet has proven proficient in detecting cloaked ships in the past. I am sure given enough incentive the Federation would be able to effectively negate this advantage.
Ignoring the fact that "canon-ly" the Federation has a tactical advantage of its own, albeit still in development. Quantum Slipstream drive.
Interesting theory, but do you have anything to back this up?
There are no official numbers how many ships any side has.
Only some made-up numbers on fansites.
Also Starfleet has a lot of ships that have little practical use in a war, that's the reason we never saw a single Intrepid in any of the battle scenes and only once on a diplomatic mission to Romulus.
Also in the "Yesterday's Enterprise" scenario the Klingons were on the verge of victory.
Since then Starfleet has advanced its technology but have the Klingons, now using newer ships like the Vor'cha and Negh'var for example.
Cloaking tech is not new and Starfleet has had several examples in its own hands to investigate.
Including the model from TOS:"The Enterprise Incident", Star Trek 4 and the Defiant's cloak.
And yet they're still hard-pressed to detect cloaked ships when the ship is properly build to work together with the cloak.
The Defiant was a failure in this regard because she had a very powerful energy signature for her size (might explain the size of the Warbirds).
The Klingons could park a whole fleet next do DS9 in "Way of the Warrior" without anyone noticing it.
Quantum Slipstream...in what way is there any canonly advantage in the hands of the Federation?