IND-CPA security of CTR mode Let's suppose CTR mode is instantiated such that the input to the block-cipher is $\langle \mathrm{IV}+\mathrm{ctr}\rangle$ instead of $\mathrm{IV}\mathbin\|\langle \mathrm{ctr}\rangle$, where $\langle X\rangle$ is the bit representation of $X$.

Will the mentioned version of CTR encryption scheme be IND-CPA secure against nonce-respecting adversaries? If not, can this be made nonce-IND-CPA secure by adding some cryptographic methods over it without altering the underlying structure?
The crucial property you want to achieve CPA security is that each combination of $\mathrm{IV}$ and $\mathrm{ctr}$ is used at most once, since you essentially derive a key from this combination and use it to encrypt the corresponding block with the one-time pad. If you choose $\mathrm{IV}$ uniformly at random from a large enough space, this will be the case with high probability for both variants you describe.

If $\mathrm{IV}$ is a packet counter, $\mathrm{IV} || \langle \mathrm{ctr} \rangle$ is still fine if you reserve enough bits for both $\mathrm{IV}$ and $\langle \mathrm{ctr} \rangle$ to exclude overflows. The variant $\langle \mathrm{IV} + \mathrm{ctr} \rangle$, however, now becomes insecure: If two packets are encrypted where the first one contains at least two blocks, the second block of the first packet will be encrypted with $\langle 1 + 2 \rangle = \langle 3 \rangle$, and the first block of the second packet will be encrypted with $\langle 2 + 1 \rangle = \langle 3 \rangle$. Hence, an attacker who knows the contents of the second block in the first packet can learn the first block of the second packet. As long as you only increment the combination of $\mathrm{IV}$ and $\mathrm{ctr}$ by one for the next block, this problem persists unless you ensure there is a large enough gap between two packets. This is exactly what $\mathrm{IV} || \langle \mathrm{ctr} \rangle$ ensures.