"Yes, characters may conjure an ally (p. 103, Street Magic). All of the standard rules for materials, extended tests, and buying hits between Missions apply." (p. 10, Missions FAQ)
The conjuring ritual for an ally spirit uses exactly the same rules as summoning and binding any other spirit...it even says so. (p. 104, Street Magic, first paragraph under Conjuring Ritual)
I see no reason why a regular summon/bind attempt should be any different. I would say, though, that if one test is rolled at the table, all relevant rolls have to be made at the table for the binding to be valid...no rolling your own Binding and making the spirit buy hits or anything cheesy like that.
Lurker, I think you're being a little too strict with the wording on the Buying Hits rule: "If the character might suffer bad consequences from failing the test, then the gamemaster should require her to roll the test rather than buying hits" (p. 62, SR4A). By that logic, you shouldn't allow characters to buy hits when acquiring gear, because they "may" attract unwanted attention from authorities, mafia, etc. on a glitch (p. 312, SR4A). "Should" is a recommendation, "must" (or omitting the phrase altogether) is a requirement. The Missions FAQ has interpreted "should" a little differently (in the cases of both buying gear and conjuring an ally spirit) in the interest of allowing characters to do stuff during downtime without hounding a GM while (s)he is trying to get food in the last 5 minutes before the next convention slot.