There are two answers to your question:
"Yes" - a person/company that is looking at helping you that is ONLY in it for the short-term money could hurt your company in various ways, e.g., doesn't get you the traffic your site needs, takes short cuts and gives your company "bad" exposure from the search engine perspective--like submitting your company's site to 1000s of useless business directories.
"No" - a reputable person/company could have a HUGE positive effect on bringing targeted (potential clients) traffic to your company's site, help get the "word" out about the products/services you are selling, optimize your site that when people do get there, they can find what they are looking for and have a good user experience.
These are just some of the tips on finding the SEO company that will help you:
1) Provides you with real examples of SEO work they've done on highly competitive search terms; gives you references that you can check.
2) Explains things in a fashion you can understand
3) As "VictorG" mentioned, doesn't GUARANTEE first page results
4) Doesn't try to "sell" you. A good SEO company explains how things work, what exactly they will be doing for you, how they will keep you updated on their progress, e.g., reports, phone calls, email summaries, etc. In other words, the way they are going to help you should be transparent vs. "give us the money and don't worry about a thing"
5) If their proposal sounds too good to be true, it probably is.
6) If you talk with SEO companies, trust your instincts. If something doesn't seem right, move on. Going back to #4, they should present you a solution and let the solution sell itself. When they start offering discounts to make a quick decision or pressure you, that is never a good start to a business relationship.
7) DON'T GO WITH THE "CHEAPEST" PROPOSAL JUST TO SAVE MONEY. Go with the company that you feel will bring the greatest VALUE.
A good honest SEO company will feel like a partner, or trusted advisor, not a rigid machine that is unwilling to compromise or adjust. If your company is paying the bill, this SEO company works for them, not the other way around.
I would not recommend a company does it on their own unless they have the knowledge and time to dedicate. Trying to find the one "how-to" guide out there that gives them all the information is impossible, because SEO is part art, part science. However, you can look to have an SEO company help guide you. In other words, they give you a blue print to follow, but you are doing most of the work...which would lower the cost...but this is only if you are 100% against having a qualified SEO company do all the work.