I do find the interlinear extremely helpful, but I would not consider it a way to learn the language from scratch. It's possible, but I'm not sure it's the easiest way... One thing that will be difficult to pick up from that is any sense of grammar - verb tenses, case endings, the quagmire which is Greek participles... An interlinear is most useful when you have a basic idea of the grammatical structure of the language, but know very little of its vocabulary. And even then, it does have its limits - the interlinear gives only one option for the word's meaning, rather than a full-size lexicon which might give a wide range of possible meanings and shades of meaning dependent on context and usage.

I don't want to dissuade you; I think it's a fine goal to dive into the original Biblical languages. Work through a basic grammar book to get a solid foundation for it, and have a lexicon at hand for comparison for any difficult words, and an interlinear will be a valuable tool.

My initial Greek and Hebrew training was through intensive courses - all day five days per week for ten weeks. It's like drinking water from a fire hose. And that was to start to grasp basic grammar and vocabulary, not to read fluently.

Edit: For a basic grammar, I've used Elements of New Testament Greek by J. W. Wenham, Fundamental Greek Grammar by James Voelz, and New Testament Greek for Beginners by J. Gresham Machen. All three are good, but I found the Machen book to be the easiest to use. That could just be a personal preference. For Hebrew, I used Fundamental Hebrew by Andrew Bartelt.

For lexicons, Brown-Driver-Briggs (BDB) is the standard for Hebrew, and Bauer-Danker-Arndt-Gingrich (BDAG) is the standard for Greek. I don't remember what the official titles are, just the scholars who compiled them; everyone just refers to them as BDB or BDAG.

Edit 2: I have the Zondervan Parallel New Testament in Greek and English which is quite good, I think. It's got both the KJV and the NIV on the left-hand page, with a Greek and English interlinear on the right-hand page. Having the very literal interlinear on one side with a more fluent English translation on the other does certainly help, though I still believe you need a little grammar background to really get something out of it.