Is the phase of the photon which photoemits the electron anyhow reflected in the photoelectron wafeunction? Imagine you have a carrier-envelope stable optical pulse. You use it for photoemission of an electron wave-packet. This electron wave-packet can be considered as a superposition of plane waves, with complex amplitudes which are in a certain relation to each-other. Does phase of the initial laser pulse enter this relation in any way? 
Experimentally speaking, if I will make two photoelectrons interfere, will the result of their interference (in space or energy) depend on the phase of the photons I used to "create" these electrons?
From the paper below it seems that the electron wave-packet is defined solely by the envelope of the pulse, and not by the carrier, but it would be really great to have confirmation:

Attosecond Streaking Enables the Measurement of Quantum Phase. V.S. Yakovlev, J. Gagnon, N. Karpowicz, and F. Krausz. Phys. Rev. Lett. 105, 073001 (2010), arXiv:1006.1827

 A: 
Does phase of the initial laser pulse enter this relation in any way?

Absolutely. If you're doing single-photon absorption (which in practice, in this context, means excitation driven by a classical field, in a regime that is linear with the driving amplitude*), then the phase of the outgoing photoelectron wavepacket will be directly given by the phase of the incoming pulse.
This is laid out explicitly in Eq. (2) of the paper you cite: when they stipulate that the photoelectron momentum-space wavefunction caused by absorbing an XUV wavepacket with frequency amplitude $\tilde{\mathcal E}_\mathrm{XUV}(\omega)$ is given by
$$
\tilde \chi(\mathbf p) = -\frac i2 \tilde{\mathcal E}_\mathrm{XUV}\mathopen{}\left(\frac{p^2}{2}-\frac{p_0^2}{2}\right)\mathclose{} D(\mathbf p),
$$
they directly specify that the phase $\arg(\tilde{\mathcal E}_\mathrm{XUV}(\omega))$ of the component at frequency $\omega$ gets imprinted onto the corresponding $\chi(\mathbf p)$, with only an absolute phase of $-i$ and the response function $D(\mathbf p)$ in the way of a direct equality between the two. (Here the dipole moment $D(\mathbf p)$ may or may not be a slow-varying function, depending on where you are in the spectrum w.r.t. various resonances.)
It's unclear to me why you think this paper suggests that the photoelectron wavepacket is 'defined solely by the envelope of the pulse', because it is certainly not the case. For the XUV pulses considered by Yakovlev et al., the spectral phase is extremely important: those pulses are typically (read: using current technology, always) generated using high-order harmonic generation, and that mechanism always produces XUV pulses with an intrinsic chirp (known as the 'atto-chirp' in the literature) whose precise characterization is extremely important and an ongoing area of theoretical and experimental research.
Perhaps you're just worried by the fact that they specify the field as $E_\mathrm{XUV}(t) = \mathrm{Re}[\mathcal E_{XUV}(t) e^{-i\Omega t}]$? If that's the case, then don't worry - the factor of $e^{-i\Omega t}$ is only a notational convenience, and the complex pulse function $\mathcal E_{XUV}(t)$ is not a pure envelope - it also encodes the more complicated details of the pulse shape, from its chirp upwards.

*This is important, of course, and you need to be in this regime for your question to make sense. If you want to work in a QED or quantum-optical formalism, on the other hand, "the phase of the photon" doesn't make very much sense if you insist that the field be in an $N=1$-photon eigenstate of the photon-number operator, which is canonically conjugate to the photon phase. The quantum phase of the state of the field then matters, but it's much trickier ground to work on. Or, in other words: be very careful with the word "photon" when you're doing things like this.
