Is cutting buckthorn (hopefully before it goes to seed) an effective control strategy?

Buckthorn resprouts aggressively in my experience, so cutting is best coupled with a stump treatment to prevent resprouting. Buckthorn seeds also remain viable in the soil for a few years, so retreatment may be necessary.

A few recent papers that came out:

No evidence of a long-lived seedbank in common buckthorn, Rhamnus cathartica L., within Minnesota deciduous forests | SpringerLink

A takeaway from this paper: deal with the female (berry producing) plants first

Using plants to control buckthorn (Rhamnus cathartica): Improved biotic resistance of forests through revegetation - ScienceDirect

A takeaway from this one: Following appropriate forms of treatment (see BMP guide) underplanting native vegetation can reduce the competitive advantage of remaining buckthorn seedlings and saplings in the understory. Suggestions from this study include sugar maple, balsam fir, canadian elderberry and dogwoods.

As a side note there are some sites where for whatever reason the landowner does not want to use herbicide. I have girdled trees below the living crown there within  ~2-3 weeks after leaf out based on the findings from this paper on the seasonal fluctuations of carbohydrate reserves in buckthorn crowns which was initially published as a thesis in the late 00's (https://pdfs.semanticscholar.org/5ab9/60778f874f3691227e229a123a255b7a1c6b.pdf) 

I have seen approximately 65% of girdled stems die in the first year and get the remainder by removing sprouts and regirdling lower on the stem in the second year.

So to answer your question, cutting buckthorn can be part of an effective control strategy when combined with the recommendations provided above by Norm, Felix and Mike and some of the emerging research I shared. How you approach it will depend on your capacity and local context. Curious to hear how it is going so far?