Is our speech affected by full mouth dental implant? (Photo)

If you see an experienced dentist or prosthodontist , you should not have a problem with speech. Placement of the implants and the Restorations over dental implants should be based on proper bite ( occlusion) which your dentist evaluates in addition to evaluating your speech ( Sometimes using temporary restorations brfore finalizing the case) 

Yes, speech alters when you have malaligned teeth, missing teeth, or spaces between teeth. Correction in these improves speech. So in your case, you have missing teeth, so after restoration definitely, your speech will improve.

If your implants are properly placed and restored, you should have no problems with your speech.  It sounds like your loose teeth are adversely affecting your speech right now, so the restored implants should improve your speech, as well as your ability to use your front teeth for biting food.