There are the standard usability concerns.
I think 'looks like' is key here. If someone is using a screen reader they will 'see' a link and act appropriately.
If someone has javascript turned off the jquery function (obviously) won't run and they will also get link behaviour.
Obviously you've already done the soul searching(!) over using a link like a button so it is a case of dealing with these two cases - screen reader and non-javascript.
If you can't also simulate the button behaviour (on a link) for these two cases then you will be offering different people a different experience - which is a good reason not to use the function. Either the spacebar should fire every use of these link/buttons or none of them.