I can only answer this from the perspective of the United States. I know three developers who had no college after high school. The other two were already working in fields related to software engineering and were able to post up. That said, the one who had no degree had to work for free for a company for a month before they’d hire him.
So a two year degree will probably make it harder for you to land your first job if you aren’t already working with a company. In the US, most two year degrees transfer immediately to four year institutions so at least here, you could finish your first year, get an internship, and if the company’s willing, you can get hired on as a programmer. Or, you can finish out your last two years and have a BSc.
Now, with all of that said, you won’t be getting equal pay to a BSc for probably 3yrs. I don’t know why that’s a magic # in the USA but generally once you have 3yrs experience working as a software engineer the piece of paper that represents your degree ceases to matter. I keep saying “in the USA” because I have heard anecdotally that in Europe, your degree matters more, which tells me that it’s harder to work your way into a position without a degree.
That exists somewhat in the USA, if you work for the government. It’s not uncommon for advancement to be capped, for example, I know in the USGS you’re not going to make management without a PHD.
Keep that in mind as well: you may want to finish the BSc because maybe in ten years you hate engineering and want to do something else. With BSc, you have the main prereq needed for a master’s degree (MSc) in an entirely different field. That path is closed to you with the 2yr option.
I don’t like taking risks, so my 2pence is to get the BSc.