Is there any point mining on a box with limited resources?

I've got a spare box that's got limited resources (e.g. 1GB RAM) that's sat there doing nothing. I like the idea of it sitting there and running as a node (may as well be doing something, rather than nothing) but is there any point in running mining on it too?

I understand that it's not going to mine a great amount, but will it mine anything at all if the specs are so low?

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