Thought I'd add a bit on my own experience.
- Back before the dawn of time I started a law degree. Absolutely hated it and dropped out after one year.
- Transferred to science. Behaved like a teenager, failed, had a major car accident and dropped out after one year.
- Three enjoyable years in retail.
- Back to science first year, no longer a teenager. Loved it to bits, worked hard and eventually got Honours in Astrophysics.
- Immediately left for finance and have had a long, interesting and happy career, while still enjoying science and astronomy as an amateur.
The lesson I have taken out of this is to choose to do what you want or like, and see where it takes you, rather than what you think you ought to in order to get to a specific end goal.
If you do something you like, you'll probably enjoy it, work hard at it, and be good at it. Once you're good at it, all kinds of other opportunities will probably open up.
Conversely, if you do something you don't like, in order to get somewhere else, it will be very hard to enjoy it, work hard at it and get good at it.
In your situation, if you think doing EE would be interesting for its own sake, I'd go for it, and if you think it might get you to astronomy, then great, but make sure you're enjoying the EE on the way. If you have no real interest in EE, though, I'd think very carefully.