Do mosquitoes need to pump blood out of the host?
Take a look at Ramasubramanian et al.[1] The authors have some great SEM images of the proboscis and fascicle tip and derive a mathematical model for the "bite" itself.

They mention that there are two types of feeding: pool feeding, where the mosquito creates a hemmorrhage and feeds slowly via capillary action, and capillary feeding, wherein the mosquito taps into a capillary and the feeding process is much faster, as the blood is driven under pressure.

Another source to check, one that the authors above cite, is by Kashin[2]. This only links to the abstract, however.  You'd have to hit the stacks to get the article, I'd imagine.



Edit

This source[3] indicates that: 


  "The blood is imbibed by action of the cibarial and pharyngeal pump muscles via the food canal formed by the labrum and hypopharynx. Blood then passes into the midgut."


For @Luke, and others:






All images are from Ramasubramanian et al.[1]


Ramasubramanian MK, Barham OM, Swaminathan V. 2008. Mechanics of a mosquito bite with applications to microneedle design. Bioinspiration &amp; Biomimetics, 3: 046001, doi:10.1088/1748-3182/3/4/046001.
Kashin P. 1966. Electronic recording of the mosquito bite. Journal of Insect Physiology, 12(3): 281-286, doi:10.1016/0022-1910(66)90143-0.
Robert V, Brey PT. 1998. Biting physiology of Anopholes affecting Plasmodium transmission. Research and Reviews in Parasitology, 58 (3-4): 203-208.