It's terrible when another language keeps slipping into your mind. I saw this as "Can I see your dogs" which meant I got my German and Esperanto and their cases all mixed up! I am trying to think in Esperanto in my daily life now but every now and again German, which I learned 40 years ago, keeps slipping into my thinking. How do you stop it? I see some people learning ten languages on Duo and I just don't know how they do it!
Is this construction natural in Esperanto? Yes, "can" is often used as an auxiliary for perception words like "see, hear, feel" etc. in English, but it is purely a grammatical quirk with little to no semantic value. In many languages I know, this sentence, translated directly, would make no sense.
No, it's not equivalent for me. This is a semantic question, not a grammatical one. Yes, there are some contexts in which being able to do something is practically the same as actually doing it - such as "I can't remember" vs "I don't remember" - but even in these cases, there is a difference in nuance. "Can" indeed has semantic value in this sentence.
- I can see two dogs, but there are some other animals there that I can't make out.
- I see two dogs, but there are some other animals there that I don't see.
The first example gives contrast between what the speaker can and cannot do. The second sentence is grammatically correct, but semantically strange.
"(capability verb)(infinitive)" is a very common—if not universal—construction among languages; it is used in English, Spanish, French, and Russian, among others. The reason we commonly tack "to" onto our infinitives in English is because otherwise it sounds like a conjugation; however, such is not really the case with our verb "be". Let me ask you which makes more sense grammatically: "It can is", or "It can be"?
From PIV it means:
To have the strength, skill or ability to do something
To have the right or power to do something
To be allowed or have the possibility to do something
So it is very much like 'can' or the german 'kann', and not really 'do' and never 'try'. 'Try' is 'provi', maybe you got them mixed up.