Yes of course it is possible but you need a LOT of time, and be willing to deal with the possibility of downmarket accommodations in outposts you had no intention of seeing, simply because of transport connections and border opening times. I assume you will be taking a lot of public transport (buses) since hiring private cars as a solo traveler will negate most of the savings you intend from not taking flights. Despite your desire to see only these particular locations, an overland trip of necessity will take time and stopping points in between your targets.

You also need to get very familiar with visa requirements for land crossings. Assuming a Western passport: Vietnam inbound--most nationalities must have in advance, no visa-on-arrival at land borders. Cambodia inbound--at most borders you can usually get, but can be a hassle (scamming) esp at the Aranyaprathet-Poipet border with Thailand. Laos inbound--usually you need in advance except at the Friendship Bridge crossing Nong Khai to Vientiane. Thailand inbound--most borders usually fine to get a visa-free entry stamp, but you only get 15 days.

Were I doing this trip overland, I'd probably fly one way from Bangkok to Hanoi, then work my way back to Laos/Luang Prabang then overland through Laos to Phonesavan/Plain of Jars, then via Vientiane get to Thailand over the Friendship Bridge, then via northeast Thailand to the Anlong Veng or O'Smach border crossing to Cambodia and Siem Reap, then back to Bangkok. The reason for this is that border crossings are less hassle and transport timing works better this way, especially in the Vietnam-to-Laos direction compared to vice versa, and also the Siem Reap to Bangkok road trip.

Time allotment: Assuming a flight to Hanoi and excluding time in Hanoi and Bangkok (endpoints), I calculate the following:
Hanoi to LP: 2 days
LP area: 3 days
Laos travel to get to, see, from Plain of Jars to Thai border: 3.5 days
Thailand northeast segment border to border: 1.5 days
Cambodia including travel to and decent time at Siem Reap area: 4 days
SR to BKK trip: 1 day.
That's 15 days. Assuming one flight at the start. And this is not a leisurely pace, but moving pretty steady and deliberately and having some prior idea of the timing of optimum intercity and border connections.

I also suggest that if you are set on doing this, that you expand your research to include the following websites and forums which will have more knowledgeable posters than the typical FT demographic for this sort of trip:
www.lonelyplanet.com
www.virtualtourist.com
www.talesofasia.com
www.canbypublications.com

IMO, if you are NOT interested in seeing interstitial parts of these countries in addition to the specific cities you mentioned, overland makes no sense. It definitely doesn't make sense to do overland in both directions. Most people doing overland both directions plan a circular route that includes more of Cambodia including Phnom Penh, plus South and Central Vietnam, and they allow at least 6-8 weeks. I think in the end, you will not save money and if you just want to see these few locations on the wish list, you should just work on finding the best discounted flight options and perhaps just do the intra-Laos part and the Siem Reap-Bangkok part overland.