Is it okay to write quotes without quotation marks if people can recognize them as quotes?
It's fine as long as the fragment stands out. Quotation marks are just one of the many ways to do that. Look at this forum, for instance. It puts quotes in a grey box, like the one at the top of my post. This makes it stand out and helps the reader realize these aren't my own words, but a quote. It fulfills its purpose.
In theory, you can use whatever you want as long as you remain consistent and it's relatively easy for the reader to understand your intention. However, it's much simpler for both the writer and the reader to just use what's already firmly established. There's no need to reinvent the wheel, you know. Everyone already understands what quotation marks are and what they're used for. Why not just use them if they're already there?
Personally, I'm not a big fan of putting quotes in bold because that's very commonly used for emphasis. There's a potential misunderstanding as to why the text's put in bold because of that, and besides, it alters how the letters look, which isn't something my bad eyesight would appreciate.
I do understand why some people might not want to use quotation marks, though. They're pretty bad at communicating that a portion of the text is a quote when the quote is very long. The reader might get lost in the text if the only clue they have is a symbol, hidden in a plethora of letters and punctuation marks. It's easier to realize which portion is a quote, especially when just skimming the text, when it's formatted like this...
Lila Mae sees Chancre swallowing the super's hands with his oversized mitts in faltering camaraderie. It takes a long time to become a politician, but he was born with the smile. You can't fake smiles like that. Nice building you got here, chum. Nice to see a man who takes pride in his craft. Sometimes you walk into these places, you never know what you're going to see, bless my heart. You want to say to yourself, how can people live like this, but then we are all dealt differently and you have to play what you're dealt. Back home, we . . . He gave 125 Walker a clean bill. Lots on his mind, lots on his mind.
...than when it's formatted like that...
Lila Mae sees Chancre swallowing the super's hands with his oversized mitts in faltering camaraderie. It takes a long time to become a politician, but he was born with the smile. You can't fake smiles like that. "Nice building you got here, chum. Nice to see a man who takes pride in his craft. Sometimes you walk into these places, you never know what you're going to see, bless my heart. You want to say to yourself, how can people live like this, but then we are all dealt differently and you have to play what you're dealt. Back home, we . . ." He gave 125 Walker a clean bill. Lots on his mind, lots on his mind.
...but in the end, there's probably an even better way to do this, but my post's already long enough, so I'll leave it off here.