Adding AC signals that are out of phase.?

You probably will get some phase difference in the two signals, but I think you are over-analysing it. I don't think it will be a problem. Acoustic signals mixing with different phases happens all the time; it happens whenever you play in a room that's not an anechoic chamber. It adds life to the sound.

Try it. If there's a problem, that's the time to start looking for a solution!

If there is a problem, e.g. if you get dead notes due to comb filtering, then one thing that might work instead of fiddling about trying to re-align the phases is to add even more delay to one channel, like 50 - 100ms. That will basically create slapback echo. It could sound really good.

What you say will happen is only meaningful when the levels of both channels are similar when added together. For example a 10mV signal cannot cancel a 100mV signal whatever the phase is, but can reduce it slightly (or increase it slightly) according to the vector sum. What other answers say about try it, and see what it sounds like, is what I would do too.

As far as answering your question, all filters add delay. Most affect frequency response too. An all pass filter is used to provide delay only. This can use R, L and C in a passive or active circuit, but has a flat frequency response in the pass band. It is unlikely you can simply provide a flat but significant delay response across the whole audio band though, many octaves.The circuit in the link here, the RC hi pass filter has a delay of R * C (its time constant). This applies to frequencies below about 1/10 the cutoff frequency of that RC filter (F = 0.1/2pi*R*C). The RC is therefore set about 10 times the frequency for the desired delay. The all pass circuit makes this delay according to 2 x RC for the same frequencies if the 2 of Rx are equal. Therefore if RC is for 159,000Hz the all-pass filter provides constant 2us delay up to about 15,900Hz. The op-amp changes this a bit because its own delay is of this order. This cannot do what you want, even with large numbers of them. A 1590Hz all pass filter provides 200us delay up to 159Hz.

http://en.wikipedia.org/wiki/All-pass_filter

A delay can be provided easily by a digital processor, which delays each ADC sample before sending it on to the DAC. The advantage of this is that it is reliable and can provide an arbitrary quality. This is the method to use. This is possibly a function provided by a looper. It uses similar hardware, with slightly different software I expect.

In the past there were analogue equivalents of this, called a bucket brigade delay line, using charge coupled devices. A similar device was used to record messages. It is a form of analogue shift register. A tape loop with a space between record and playback head was used before that. There were other delay lines using sound waves along springs. These ideas were used to provide the delay for echo and reverberation.

A length of wire can provide a delay, but 4ms delay from a roll of coaxial cable requires a length like 720km, hardly practical.

"Will I have any phase cancellation isssues or comb filtering? If so, how can I correct the phase to match them again?"

Yes and no you can't (without elaborate stuff you can't do in real time in performance.) Make it up, get the weird sounds and see whether you like them - if not, don't use them.