Ignoring my play on words attempt, to answer your questions (sort of)...
It really depends on whether you are pushing the fluid through the test section or pulling it through. Almost every wind tunnel does the former because it is much more important to control the flow conditions as it enters the test section (among other factors.)
It's much tougher to do so with a "suckdown" tunnel - compared to a "blowdown" facility.
Regarding the latter, most, but not all, of the largest ones rely on stored fluid (compressed air), typically pressurized using large turbomachinery. A valve is opened (and regulated) and the fluid (usually air) passes through a series of devices to "clean" and smooth it before it enters the test section. That "turbomachinery" could be reciprocating pumps (think greatly scaled-up shop compressor!) Whether than makes "sucking" a prerequisite or not? If any and every action of taking a fluid from a low to a high pressure means sucking must be involved then I guess I'd agree - although we tend to think of sucking device (in an engineering sense) being much more active than that; usually with a tapered / designed nozzle that maximizes the sucking ability - rather than a device where we simply want a wide open inlet. In any case, once the storage "bottles" are filled, the tunnel is essentially independent of and from the turbomachinery.
I guess the point is more debatable in the case of closed circuit "race track" type wind tunnels where the "fan" is directly in the flow loop. However in that case most everyone agrees that the flow is being blown, not sucked through, the test section. Why? Because in all such cases there is a an expanded section ("settling chamber") directly after the test section where the flow speed is greatly reduced before it then begins its trip back around. There is therefore essentially no sucking effect - it's all blow.
In any I think we can all agree that CHUCK SUCKS AND BLOWS!
Jeff