Citrus grow nothing like the other plants you are comparing it with (honeysuckle, vines, etc). The answer is Yes, I'm sure citrus can be done (as the picture above shows). I've seen other pictures like above and talked with one person who did some strange training on his citrus. But you'd be fighting the tree the entire time and you'd want to get some resources on advanced training, which are fairly scarce except for the basics on cordons, espaliers, etc. The Eureka lemon (and many grapefruit) are good possibilities as their shoot elongation can be larger, especially when they are given extra Nitrogen. There are also methods of using partial shade to elongate branches and trunks. The Eureka can grow very long limbs (and trunk) in many circumstances, which would be required to train it as such. On my Eureka, I've removed many vertical branches that were over 15' tall with only 1 major side branch on it. Typical orange trees won't cooperate easily and neither would mandarins. Additionally, I've read the sweet oranges can be fussy and not fruit consistently with constant training work that would be required. But none of this should scare you away. The Eureka will produce even more beautiful flowers/scent than the orange you saw at the nursery. Since you state to have the patience needed, go for it. You'll need to find the resource to learn from. Mainstream books will be limited to the the most common easiest training methods. Or take a trip to Lotusland and talk with their staff! ;-)

Before you go to the trouble and expense of figuring out a support system and planting the vines, I'd check with your local municipality and utility/phone companies as to whether they'll permit such plantings. In my area it is illegal to plant anything on telephone or utility poles - it interfers with maintenance - and it is very difficult to get any vine to establish on a smooth metal pole. They also heat up alot in summer, effectively cooking the vine.

The pergola in the picture does not look like one you would actually plant something on! Where would you plant the vine?! The posts are too far from soil/ a planting bed where you could plant something, so unless you plant annuals in big pots, the structure is a stand-alone thing to provide shade (if necessary you could add shade cloth to the top, or a finer lattice or patterned metal-work to the top to increase the degree of shade...) Is your pergola that far away from a planting bed? Naver grow a wisteria unless you are fully aware of - and prepared to do - the degree of pruning required to promote maximum flowering and contol of the vines. Is that something you're prepared for?

Annual vines sound good to me. A mix of morning glories and moonflowers would be gorgeous.