Hi Almummy. I don't have a Pomegranate tree, so I'm not sure how useful my post will be! But as you don't have any replies yet, here goes...The pomegranate tree does require bees for pollination to produce fruit, so the flowers would certainly be attractive to them.
Any shrub or tree with flowers followed by fruits/berries is likely to attract bees for pollination in a similar way, and berries and fruit might also attract rodents.
I can think of two alternative strategies for your mediterranean themed garden.
Firstly, you could choose a different type of shrub or tree that is a sterile or, almost sterile, hybrid variety. It will produce flowers but little or no pollen/nectar so won't attract bees. This will also mean no berries/fruit, so not tempting for rodents.
You can do your own research into this, but there are two types of such plant I can think of - although not mediterranean, they might blend into such a garden sufficiently to not look out of place, depending on your preference.
The honey locust sunburst tree (Gleditsia triacanthos f. inermis Sunburst). It's a beautiful delicately leaved tree, grown for it's foliage. Rarely are the small flowers fertile, and I have never seen it produce seed pods. It can grow up to 25 ft but this is likely to be after 30-50 years growth. It is thornless.
I have grown the sterile shrub Viburnum (plicatum f plicatum) as a standard tree shape. It is less likely to blend in to the mediterraneam theme but would be very striking! Its white flowers are similar to a lacy hydrangea, and it has interesting colour foliage in autumn.
Secondly, you could choose a shrub that is grown for its foliage, and just trim off the flower buds before they develop. Photinia red robin might fit well into your garden as thrives in a sunny site. When it is grown as a shrub it is rather dense, but when trained as a standard with a single trunk, it has quite an open, attractive habit and it easy to prune. It can also be bought as a top grafted lollipop tree in various heights. If kept pruned to this shape it will not flower or fruit. It is evergreen.
Apologies if this is not what you are looking for!