It will go through, and might get canceled within a minute under some higher fee conditions. If it survives that long, it probably will persist on large mempool nodes for a long time, and find its way back to normal sized mempool nodes when fees are very low. Mempool.space would seem to indicate that most nodes are canceling anything under 2 sats per vbyte, so propagation through the network would be hit or miss unless you run your own node with a mempool that's prioritizing or otherwise keeping your transaction in it.