Can ovulation and menstruation occur simultaneously?
Ovulation and menstruation don’t happen in normally cycling women at the same time. A basic outline of the hormonal cycle that triggers these events will make this clear.

Proliferative (a.k.a follicular*) phase
Beginning after menses (when the endometrium is thinned), the hypothalamus produces GnRH which stimulates the anterior pituitary to produce LH and FSH. These in turn stimulate ovarian follicles to develop. A dominant follicle produces estradiol which causes the endometrium to thicken (proliferate).

At a certain level of estrogen (actually estrogen/progesterone ratio), the feedback on the hypothalamus flips from a negative to a positive feedback loop. Thus, there is a GnRH followed by a LH surge. The latter triggers ovulation. Note that at this time the endometrium is stable due to relatively high estrogen levels. 

Secretory (a.k.a. luteal*) phase
After ovulation, the high levels of LH trigger formation of a corpus luteum from the tissues left behind after ovulation. The corpus luteum makes progesterone. This hormone triggers a change in the endometrium from a proliferative to a secretory state. Progesterone also provides negative feedback to the hypothalamus and anterior pituitary, maintaining low levels of GnRH, LH, and FSH, so no new dominant follicles develop at this time.

If pregnancy does not occur, the corpus luteum will eventually (10-12 days) degenerate and stop producing progesterone. It is this abrupt drop in progesterone that triggers the sloughing of the endometrial lining. You can see these hormone shifts in an illustration like this: 



The decline of the corpus luteum is correlated with a decline in serum levels of ovarian hormones including progesterone, estradiol, and inhibin A. Release from negative feedback provided by these hormones at the level of the hypothalamus and pituitary permits FSH to rise, and the cycle begins again.

You should now be able to see that: 


Around the time of ovulation, the uterine lining is not fully developed and is stable due to the hormonal milieu. Menstruation does not occur.
Around the time of menstruation, FSH and LH are suppressed in a way that is not conducive to ovulation. 


In theory, yes, of course there would be a lower chance of initiating a viable pregnancy (implantation rather than conception is the most obvious problem) were the endometrial lining to be unstable at the time of ovulation. The problem of luteal phase deficiency is along these lines. In this condition, the corpus luteum does not produce adequate progesterone during the luteal phase to develop the endometrial lining in such a way as to support a healthy pregnancy. However, ovulation and menstruation are still time-separated events for the reasons outlined above. 

*Note that the first term is with respect to the endometrium; the second is with respect to the ovary.



Abbreviations:

GnRH - Gonadotropin Releasing Hormone; LH - Luteinizing Hormone; FSH - Follicule Stimulating Hormone
  

References

1. Anatomy &amp; Physiology, Connexions Web site. Illustration is also from here.


2. Jerome Strauss, Robert Barbieri. Yen &amp; Jaffe's Reproductive Endocrinology. September,  2013. Saunders.