Do pages with irrelevant keywords hurt the domain overall for ranking for relevant keywords?

[SNHU]

I have been doing SEO for the University I work at. We are optimizing our degree pages on a page-by-page basis. So hypothetically we have a page optimized for "online accounting degree" and another for "online marketing degree", etc. Although our focus is on specific page optimization, we hope the by-product is that the whole domain will   start to rank better for "online degree".

First of all, is this a reasonable expectation?

Second, if this IS the case, will pages full of irrelevant keywords hurt the overall strategy? For example, our registrar and financial aid PDFs that are full of legal/financial mumbo-jumbo. Are these lowering our keyword density of relevant keywords across the domain?

[EGOL]

I agree, potential students will likely be searching for specific degrees by academic field.

The page that is optimized for "online degrees" will be the page that high schools, businesses, other universities and education portals will be linking to most often.  When these programs are marketed the marketing materials could invite links to this specific page.

[Hurf]

I would bear in mind that most people who are serious about undertaking an online degree are likely to search for an online degree in a specific field - Online Marketing Degree etc, rather than the very vague 'Online Degree', so I would target one main keyword (and related keyword variations) per page/discipline.

Potential customers who are further down the buying funnel will use more specific searches to find exactly what they want - afterall, they will know that a search for online degree will bring out LOTS of irrelevant results and not deliver what they are looking for - so they drill down using the long tail keywords.

Take a look at The Long Tail by Chris Anderson - http://www.amazon.com/Long-Tail-Revised-Updated-Business/dp/1401309666/ref=sr_1_2?s=books&ie=UTF8&qid=1308771559&sr=1-2

You will also stand a better chance in the SERPS targeting the longer tail keywords.

It's easy to get blinded by numbers in SEO and it is very easy to all end up chasing the same keywords - when they might not be the best converting keywords - I have spent some years doing exactly that and it is only in recent years that I changed my tactics and started pursuing 'more of less' and as a consequence improved the performance of my online business considerably.

If by 'irrelevant keywords' you mean the words that occur naturally when discussing your subject area then it is absolutely not an issue if you provide quality information, written for the reader primarily - not the search engines. It is easy to get blinded by focusing on nothing other than keywords, which usually results in their overuse in an unnatural and spammy looking way.

Remember - Search Engines won't buy what you are selling - but your visitors will - IF you can show them ithat you offer what it is they are looking for using tried and tested sales copy, which is reassuring and can demonstrate the product features which will benefit your visitor/potential customer.

[EGOL]

we hope the by-product is that the whole domain will   start to rank better for "online degree".

I have a website that has a lot of content about a specific topic.  As that site has gained content and links from other websites in that topic area I believe that the domain as a whole has gained ranking strength in that topic niche.  I don't have a formal study to support this but I simply see that new pages seem to rank easily in that niche.

In your situation, your domain might gain strength for "online degree", however, it will still remain in competition with other educational websites who are doing the same thing.  So unless you are becoming the gorilla in that niche I would not expect this alone to put you on the first page of Google for "online degree".  You will have to earn that ranking by producing an optimized page for that term and through the force of domain authority and inbound links to that page.

will pages full of irrelevant keywords hurt the overall strategy?

No.  Almost every site has this type of content.  Think about all of the other stuff that exists on .edu domains.

Good luck with your work.  I did the same thing a long time ago when online courses were very new (and search engines were very different)