Basically it depends on if it can handle the heatload of the system you put in it. I don't know anything about a lab freezer, but I would guess it's just a freezer that is designed to take things to lower temps and hold them at a more regulated temperature. NOT designed to get it to that temperature very quickly. And that is the problem, if it cannot remove that heat quickly, the computer system inside is still going to produce heat more quickly than the freezer can remove.
OK, here is a slightly elaborate analogy that hopefully gets delivered in an understandable way...
Let's say you were trapped in a small room and that room had an opening in the top that was being filled with sand. But you have a vacuum hose in there that can help you suck up the sand and send it outside of the room. Basically, if that vacuum hose is not capable of sucking out as much or more sand than what is being put IN the room, you are eventually going to suffocate when the room fills with sand. It doesn't matter that you have a vacuum that is slowly removing the sand because there is way more sand coming in than it can take out.
This applies in the same basic way to a freezer. If there is a heatsource in the freezer, the freezer's cooling system can transfer that heat to the outside of the freezer. As most freezers go, they could ALL remove that heat eventually, it's just a matter of how fast they are designed/capable of doing so. But the trouble is, if that heatsource is still creating MORE heat, you run in to the problem of more sand(heat) going into the freezer than the freezer's "heat vacuum" can remove.
Does that make sense?
Perhaps if you could find some kind of flash freezer or something that is designed to quickly remove heat, maybe that would stand a better chance. But you have to know the capabilities of the freezer in how many watts of heat it can remove and then know how many watts of heat the computer system will create.