Can wild rabbits raised as a baby be good pets?
The answer is probably not. You can generally raise an animal from a baby to not fear humans. But domesticated animals, including rabbits, have been specially bred to reduce the factors that make wild animals dangerous.
Domestication is when humans take a plant or animal species and,
through selective breeding, transform the species into something
beneficial for humans.
A single wild animal can be tamed if it is captured at a young age and
raised with a lot of careful human nurturing. But this is strictly an
acquired trait, and a single taming does not suddenly make the entire
species domesticated. SOURCE
Tamed just means that it does not fear a few specific humans not that its natural instincts and needs have been suppressed. You can may even be able to teach it some tricks, but it will still have the natural needs and instinctual fears. One of those is that humans should be feared.
Rabbits are very scent oriented. Their sight is highly attuned to movement and basic shapes rather than visual recognition. A new persons scent is found the rabbit will not have been trained to trust that scent and will likely be very afraid.
Rabbits have 100 million scent cells, making for a very keen sense of
smell, which they use to identify other rabbits and animals. The nasal
membrane is very sensitive to perfumes, chemicals and dust, and these
agents can cause upper respiratory problems for the rabbit.
The rabbit's sense of smell is far more developed than that of the
human. Moveable folds inside the rabbit's nose assist in the detection
of scent. The sense of smell in a rabbit is present at birth, allowing
a newborn to find his mother's teat. Rabbits shift their noses up and
down when trying to identify a scent; this is called "nose blinking. SOURCE
We have other rabbits will the wild rabbit present any risks to them?
As James and Xiaohouzi pointed out in their excellent answers wild rabbits are exposed to parasites and diseases that domestic rabbits are not. A baby rabbits immune system has been boosted by drinking its mothers milk so it has transferred resistance to some of them that a domestic rabbit does not have. And once the it stops drinking mothers milk it will not have it either.
The most likely potential disease to cause infant/weanling mortality
is mucoid enteritis. Although it does occur occasionally in weanlings
who have been fed by their mothers, it is seen much more often in
hand-fed babies and those who are removed from their mothers before
eight weeks of age. It manifests as severe diarrhea, anorectic
behavior (refusal to eat) and may contain blood or mucous. It also
causes bloating and gas.
Mucoid enteritis is caused by a pathogenic bacterial overgrowth,
usually of Clostridium spiroforme, in the hindgut (cecum) of the baby,
as the normal microflora are attempting to establish. These normal
microflora help the baby achieve adult digestive capabilities.
Adult rabbit stomach pH is 1-2, but a neonates' stomach pH is much
higher; the stomach and gastro-intestinal tract of neonates is also
sterile (containing no living microorganisms.) As babies wean off of
milk onto adult solid foods, the gut pH gradually changes by getting a
lot of help from the mother's changing milk constituents.
By ten days of age, the babies eyes will have opened, and they will
begin eating their mother's cecotropes, (also called "night feces" or
"cecal droppings"). Cecotropes help provide the babies with essential
nutrients and later, inoculate the hindgut with the essential flora
that is needed to metabolize a diet that is changing from milk to
solid foods. SOURCE
Do I need to feed the wild rabbit any differently than a domestic rabbit?
Yes. Domestic rabbits have been bred to thrive on a diet of pelletized food and hay. Wild rabbits need more diversity and different food stuffs than its domesticated counterparts. Be aware that even domestic bunnies that have to be hand fed(with in the first 3 weeks) have a 90% mortality rate. If you insist on trying to save a wild baby bunny, this paper from Univerity of Miami is an excellent guide. But as the paper notes you and the baby will most likely be better off if it is turned over to a animal service for treatment.