The short answer is no.
The longer answer is that linux user API doesn't support accessing files by any method using the inode number. The only access to the inode number is typically through the stat() system call which exposes the inode number, which can be useful for identifying if two filenames are the same file, but is not used for anything else.
Accessing a file by inode would be a security violation, as it would bypass permissions on the directories that contain the file linked to the inode.
The closest you can get to this would be accessing a file by open file handle. But you can't run a program from that either, and this would still require opening the file by a path. (As noted in comments, this functionality was added to linux for security reasons along with the rest of the *at system calls, but is not portable. (yet? standards evolve.))
There's also numerous ways of using the inode number to find the file (basically, crawl the filesystem and use stat) and then run it normally, but this is the opposite of what you want, as it is enormously more expensive than just accessing the file by pathname and doesn't remove that cost either.
Having said that, worrying about this type of optimization is probably moot, as Linux has already optimized the internal inode lookup a great deal. Also, traditionally, shells hash the path location of executables so they don't have to hunt for them from all directories in $PATH every time.
