I believe you can. You can set up Wordpress as the response above indicated. To incorporate, say, Google Adsense, I believe you simply insert the code into your Wordpress template.
For instance, you could create a DIV tag, style its appearance and position, and insert the Adsense code in the DIV tag. Or place the code in the right column above or below the list of your blog's pages. To pull this off, though, you will have to understand HTML, CSS and perhaps PHP, as you will be hand-coding.
I've never done it with Adsense, but I have inserted elements into my Wordpress template which then automatically shows on all pages, so the principle should be the same.
You'll be targeting your active theme's header.php, footer.php, page.php, and sidebar.php pages, plus the accompanying style.css file. The default Worpress theme path is:
/wp-content/themes/default/
in your Wordpress install folder.
To your "Additional Details":
Yes, you can continue to add more ads, if they work on the same principle of giving you raw code to copy and paste into your site. For instance, in your sidebar.php, you could add DIV tags - one for each ad service you wish to use - within the parent DIV on that page and paste your code into each DIV tag you created. The advantage to customizing the themes is that the content simply exists on every page that is henceforth created on that theme (if you change your blog's theme, you'd have to customize the new theme too).
If you do not wish to "tear apart" the default theme, you could also duplicate its folder, give this a name (e.g. mytheme), and install this new theme instead and make your edits on the templates of this theme. The key again is being able to hand-code yourself, unless modules are out there that will do the job automatically (and I'm not aware of one for this purpose).