TL;DR: Possibly. The parasite M. ancylivorus was commonly used as an organic pest-controller in 1930's - 1950's North America.

Although I have been unable to find any official statements regarding the lifecycle, writer Dan O'Bannon's original lifecycle was very similar to the parasite M. ancylivorus.

1. Adult lays the egg on a host
2. Egg hatches the parasitic larva, which burrows into the host
3. Larva uses host to gestate & form cocoon
4. Juvenile version of adult insect hatches from cocoon

This is nearly identical to O'Bannon's original Xenomorph lifecycle:

1. Adult creates the egg
2. Egg hatches the face-hugger, which finds a host & implants embryo
3. Embryo uses host to gestate & grow
4. Juvenile version of adult Xenomorph hatches from host

Note that the extra "phase" of the Alien Queen was introduced in the sequel, with which O'Bannon had no involvement. James Cameron felt that Ripley needed an "equal" to face in the film's climax, and subsequently designed the giant Queen to fit that need.

TL;DR: Not entirely. The Xenomorph lifecycle appears to be a mash-up of several actual lifecycles - mostly insects & parasites, yet isn't 100% identical to any particular one.

Writer Dan O'Bannon's original lifecycle was based on a variety of different insects, and was also very similar to parasites like M. ancylivorus.

1. Adult lays the egg on a host
2. Egg hatches the parasitic larva, which burrows into the host
3. Larva uses host to gestate & form cocoon
4. Juvenile version of adult insect hatches from cocoon

This is nearly identical to O'Bannon's original Xenomorph lifecycle:

1. Adult creates the egg
2. Egg hatches the face-hugger, which finds a host & implants embryo
3. Embryo uses host to gestate & grow
4. Juvenile version of adult Xenomorph hatches from host

In fact, O'Bannon has said that parasitic insects were his primary inspiration:

When Dan O’Bannon started conceptualising his alien creature he turned to two key influences: the creatures depicted in the comic books he devoured as a child, and the insect world. “Works of fiction weren’t my only sources,” he explained in his essay Something Perfectly Disgusting. “I also patterned the Alien’s life cycle on real-life parasites … Parasitic wasps treat caterpillars in an altogether revolting manner, the study of which I commend to anyone who is tired of having good dreams.”...

and director Ridley Scott has also quoted insects as the inspiration behind the creature:

In the 1999 DVD commentary, Ridley Scott explains: “The whole notion of this [creature] was taken off a certain kind of insect that will find a host, lay its eggs, and then in that host it will bury its eggs, and then of course the eggs will grow and consume the host. So that’s the logic of it all. Probably what makes a lot of nature go around.”

Note that the extra "phase" of the Alien Queen was introduced in the sequel, with which O'Bannon had no involvement. James Cameron felt that Ripley needed an "equal" to face in the film's climax, and subsequently designed the giant Queen to fit that need. The Queen concept does, however, stick with the same insect motif.