Are there any methods to perform the NBO analysis of a complete molecular system as a single unit (metal and ligands combined)? While performing NBO, metal and ligands are considered as separate units. Is it possible? If yes, please explain.
I'm sorry but I don't understand the question. NBO is generally used as a scheme to calculate localized partial charges that agree to some extent with "chemical intuition". This is done via a specific rotation of the basis set composed of the delocalized canonical molecular orbitals. Those orbitals are, in principle, delocalized over the entire molecular structure. However, there's no one "right" way to partition those orbitals so as to localize charge on a single atom or group of atoms, so people came up with Mulliken (useless, don't even bother), NBO(based on properties of the density matrix), Vornoi, Hirshfeld(partition space around atoms according to certain geometric principles), Bader (partition space according to the topology of the charge density) and more. These are all ways that people have come up with to obtain localized charge information from delocalized molecular orbitals if for no other reason than that chemists like to think in terms of discrete bundles of charge interacting with one another.
In your case, it's not clear to me what you're after. Any scheme you use will integrate to the total charge of the system(anion, neutral or cation), so you must be after charge properties of some subgroups within the molecule, right? I'm assuming that there's some lack of symmetry that won't allow you to divide the charge on your metal atom among the ligands? A more detailed question about what exactly you're looking for would be helpful.
Be careful with putting too much meaning into "covalent" and "ionic", as they are fuzzy concepts outside of something like valence bond theory. You can talk about where electron density is energetically preferred and such, but calling something "ionic" versus "covalent" doesn't really say too much and if you use it as a causal argument you're verging on reification.
That said, you can get this information from NBO. Here's an example from AlH3 and AlF3:
1891 (Occupancy) Bond orbital/ Coefficients/ Hybrids
You can look at specific bonds and see in which case a Natural Bond is more centered on one atom relative to another. In this case, The Al-H bond is about two thirds on the H while the same bond in Al-F has 91% on the F. You can find this in the output of pop(nbo,savenbos).