No you would not. the bitterness would be diminished slightly following prolonged boiling, but it would be hardly perceptible.
Now before I go any further, someone will soon appear on here and tell both of us that lemon and lime are sour NOT bitter. Whilst this indeed the normal perception of the fruit, it depends on such things as whether we're discussing the fruit as a whole, the juice, and even the zest of the fruit and/or it's mesocarp. Try blending an entire fruit in a food processor and taste the outcome.
Bitterness in citrus fruits is predominantly due to compounds called limonoids, around which 35 have been identified. Almost all limonoids are very bitter and are a type of compound called triterpinoids, all of which are insoluble in water. You simply cannot boil them out of fruit.
The peel of lemons and limes contain a limonoid called limonene, which gives the fruit their distinctive odour when combined with other non-limonoids such as citronellal and various terpineols. However, the white mesocarp of the fruit, contain a related limonoid compound called limonin, which is bitter along with other bitter non-limonoids such as coumarin and flavone glucosides.
(continued)