They gain only limited magical abilities:
Run Faster, p. 141, emphasis mine:
All Infected are dual natured and may freely learn the
Assensing and Astral Combat skills. Unless they’re magically
active, however, they cannot learn or use skills linked
to the Magic attribute. Neither can they astrally project,
bond foci, or initiate. An exception to this is given by the
Magical Guard power, which enables the Infected character
who has it to learn the Counterspelling skill.
(Magical guard is described in Street Grimoire (power description) and Run Faster (Karma cost))
Since you can't default magic skills, that means no spells for the
So the character gains the ability to astraly preceive, can learn to interpret his/her observations and defend him/herself against attackers from the astral plane and could learn to counterspell, if (s)he takes the appropriate positive quality, but can't learn to cast spells or rituals or summon spirits and can't even use a weapon focus.