View output a custom designed teaser then full post separate design
Sure it is possible.For that you need to add custom field in your content type called featured image.
While creating the views use that field first and you can have to add

float: left;


In Image field css class to align it left 

For exmaple you can see my site www.techiestuffs.com which is exactly what you mentioned.The teaser has image aligned left and when you click either image or title it will leads to original content.
see the below css code i used to achieve this

  .view-recentarticles .views-field-field-image {
float: left;
padding: 3px;
border: 1px solid #C9C9C9;
white-space: nowrap;
margin-right:10px;
margin-bottom:5px;
}
.view-recentarticles {
padding:5px;
border:1px solid #ccc;
background-color:#ffffff;
}

.view-recentarticles .views-field-title {
  margin-bottom: 10px;
  padding-left:10px;
  font-size: 18px;
  line-height: 1.4;
  font-weight:bold;
  background-color:#f4f4f4;
  }
  .view-recentarticles .views-field-title a {
  transition: all 0.2s;
  -moz-transition: all 0.2s;
  -webkit-transition: all 0.2s;
  -o-transition: all 0.2s;
 }
 .view-recentarticles .views-field-title a:hover {
  color: #181818;
 -webkit-transition: all 0.2s;
  text-decoration: none;
  background-color: #f6ecdd;
 }
  .view-recentarticles .views-field-body {
  padding-bottom:5px;
  border-bottom:2px solid #f4f4f4;
  }
    .view-recentarticles .views-field-field-blog-author {
    font-size:10px;
    font-weight:bold;
  padding:5px 2px 5px 2px;
  background-color:#f4f4f4;
  }