Usually, you would rather say "Es geht, die Uhr zu reparieren". More common would be to say "die Uhr is reparierbar" or "Man kann die Uhr reparieren".
If you want to use "bekommen", the sentence would be "Die Uhr ist repariert zu bekommen" which would be ambiguous though, since it could mean that it is possible to get it fixed (stressing the possibility) or that it is possible to get a fixed version of it (i.e. at a garage sale). Most of the times, it is the first variant, though.
As a question, it would be "Bekommt man die Uhr noch repariert".
Answering your question: In your example. it is possible to construct an eqivalent sentence with "bekommen", but you cannot simply switch the words.
BTW, in regards to "geht es" as possibility, this holds always true, as you can use the construct "bekommt man es hin, dass". "Gehen" as going or walking cannot be replaced through "bekommen".