The Linksys 54G Speedbooster accelerates communications by reducing the error checking/corrections and verification protocols being transmitted and correspondingly increasing the transmission of the data stream (A/B/G are made up of 2 comm streams - data and verification). Consequently, the Linksys speed booster will not interfere with any other channels on the same spectrum. This is in contrast to the DLink protocols that channel bond. Channel bonding literally merges to channels together (10/11), (5-6) etc. to accelerate transmission. Channel bonding is known to cause havoc on other wireless links operating on same frequency. In other words, you increase speed but clobber everyone around you, including any other access points you might have. I would not recommmend any product that channel bonds.
To answer your question: Yes, Speed Boost will increase the signal significantly.
Connecting two boosters? I assume you mean that you have a non-wireless router and want to attach 2 access points. Assuming you are using different channels (6 and 11), there will be no problems though you might experience interference with your cordless phone if you have 2.4Hz. If you are intending to have your APs on same channel, won't be an issue since the protocols do distinguish between APs.
In fact, I have multiple APs using different protocols (B & G) all operating at 2.4Hz without interference. Trick is different channels plus different SSID names.
Always remember to change your default password, SSID and activate WEP or WPA. Otherwise, I might be wardriving by your home and thanking you for free bandwith