Q: Will this update fix speed issues with older Macs since El Capitan upgrade?

quick answer: no.

you can see the changes here: About the OS X El Capitan v10.11.3 Update - Apple Support

But there may be other causes:

please download the   etrecheck app from    www.etrecheck.com

run it and post the list here.

Don't expect a system upgrade to solve performance problems. More likely, it will make the problem worse.

When you see a beachball cursor or the slowness is especially bad, note the exact time: hour, minute, second.  

These instructions must be carried out as an administrator. If you have only one user account, you are the administrator.

Launch the Console application in any one of the following ways:

☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)

☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.

☞ Open LaunchPad and start typing the name.

The title of the Console window should be All Messages. If it isn't, select

          SYSTEM LOG QUERIES ▹ All Messages

from the log list on the left. If you don't see that list, select

          View ▹ Show Log List

from the menu bar at the top of the screen.

Each message in the log begins with the date and time when it was entered. Scroll back to the time you noted above.

Select the messages entered from then until the end of the episode, or until they start to repeat, whichever comes first.

Copy the messages to the Clipboard by pressing the key combination command-C. Paste into a reply to this message by pressing command-V.

The log contains a vast amount of information, almost all of it useless for solving any particular problem. When posting a log extract, be selective. A few dozen lines are almost always more than enough.

Please don't indiscriminately dump thousands of lines from the log into this discussion.

Please don't post screenshots of log messages—post the text.

Some private information, such as your name, may appear in the log. Anonymize before posting.

When you post the log extract, you might see an error message on the web page: "You have included content in your post that is not permitted," or "The message contains invalid characters." That's a bug in the forum software. Please post the text on Pastebin, then post a link here to the page you created.

If you have an account on Pastebin, please don't select Private from the Paste Exposure menu on the page, because then no one but you will be able to see it.

Your question implies that El Cap runs slowly on older machines.  Not so, i have tow older machines and it runs faster than 10.9 or 10.10.

Machines that are slow typically have other problems, most often incompatible 3rd party software, and the worst culprits there are useless anti-virus programs.

Read some of the threads and learn what has been said many times already.

Grant