Not really, given that you can quite easily filter emails that you receive from your other address. I use exactly this workflow and it's much more useful than having them in separate inboxes (i.e. doesn't "defeat the purpose").
I tried it and found I constantly was sending email from the wrong account. While that's on me, it was evident I was never going to get it right either, so I went back to separate accounts.
To do the trick, you have to add the account as "not an alias" (you will have to add the gmail smpt and so) and later, select the reply "Reply from the same address to which the message was sent".
I did that. It was remembering to switch the account when composing new messages. I ended up sending work emails from my personal account on a few occasions.
Just in case you didn't see it, and weren't just talking about composing new emails, there is an option in the settings to send replies from the account that received the email.
Thanks. That was a very handy feature. Alas, it was when composing new emails. I'm sure with more diligence it'll come as second nature. But when rapid firing through emails I'd sometimes send from the wrong account and end up in confusing and embarrassing situations.