I believe that if we have two or more external sound cards, hence clock would vary for each device.
...clock would vary for each device.
Unless you can afford high end studio devices that can synchronise to a common clock, this is taken for granted. However, saying that, you also need to balance your requirements. If you are using a relatively good "audio interface" (i.e. not a random off the shelf sound card) then you can expect a pretty accurate clock. Beyond this, the question would be: What is it that you do that requires audio synchronisation down to $\frac{1}{48kHz}$ seconds? I am taking 48kHz as a minimum for an audio recording here.
How will this affect the latency?
The latency of each audio interface remains the same as before.
Will it increase or decrease? How will the factors like sampling rate, sampling time, SNR and voltage reference impact latency?
For the latency to increase, you would have to introduce some sort of relationship between the audio interfaces. Instead, both are controlled by the same source and as far as each other is concerned, they operate in isolation. All they receive is a command ("start recording") and from there onwards, it is up to the computer/drivers/OS to be fast enough to serve the streams of data produced by each.
Sampling as far as each one of the interfaces is concerned is not affected. For the system overall, you might run into problems if you request the shortest buffer with the highest sampling rate but this then is up to the system the interfaces are attached to. For a given system you might have to try a few different settings to find the better one.
It is interesting that you mention SNR and voltage reference. The SNR of the signal path has nothing to do with the clock path, so, no influence there. Typically, the reference voltage (presumably of an ADC (?)) is inaccessible to you, so, again, no influence there.
If you are so worried that you might get some sort of phasing in the background because of the synchronisation, keep a "beeper" handy (like a clapper, but just for audio and even more accurate). After you hit "record", sound the beeper so that it is recorded through all channels (or at least through two groups that belong to the different interfaces you are trying to sync). Then, when the time comes to put everything together, just make sure that the beeper signals are aligned as best as possible in the beginning of the recording. From that point onwards, assuming good clocks for the individual interfaces, the recordings should remain "locked".
Hope this helps.
